Ayo, kita belajar bersama-sama materi tentang rumus Teorema Pythagoras, cara menghitungnya dengan mudah, hingga sejarahnya di artikel Matematika kelas 8 ini!
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Apakah kamu pernah mendengar Pythagoras? Ia merupakan seorang matematikawan dan filsuf Yunani yang dikenal sebagai “Bapak Bilangan”. Salah satu peninggalannya yang bersejarah, yaitu Teorema Pythagoras!
Di artikel kali ini, kita akan belajar sama-sama mengenai Teorema Pythagoras. Apa sih Teorema Pythagoras itu? Dari mana asal-usul rumus Teorema Pythagoras? Seperti apa ya cara menghitungnya? Nah, langsung aja simak pembahasan berikut ini, ya!
Layaknya Hukum Newton yang ditemukan oleh Sir Isaac Newton, atau Hukum Archimedes yang ditemukan oleh Archimedes, kebanyakan dari kamu mungkin mengira kalau Teorema Pythagoras juga ditemukan oleh Bapak Bilangan satu ini, deh.
Nyatanya, Pythagoras bukanlah penemu pertama dari teorema ini, loh! Loh, kok? Kenapa bisa ya, bukan orang yang menemukan, tapi namanyalah yang digunakan untuk teorema ini? Mari kita simak sejarahnya, guys!
Sebenarnya, Teorema Pythagoras sudah digunakan sejak lama, yaitu sekitar abad ke 1900 – 1600 SM oleh bangsa Mesir, Babilonia, dan Cina Kuno. Mereka sudah memiliki pemahaman mengenai relasi (hubungan) antara sisi-sisi segitiga siku-siku, jauh sebelum Pythagoras lahir.
Salah satu bukti sejarahnya, yakni penemuan tablet milik peradaban bangsa Babilonia. Pada tablet tersebut, tertulis banyak kombinasi 3 angka yang memenuhi syarat Teorema Pythagoras. Kalau sekarang sih, kita menyebutnya dengan Triple Pythagoras. Diperkirakan bahwa pengetahuan inilah yang mendasari bangsa peradaban kuno untuk membangun piramida.
Namun, Pythagoras juga tidak semena-mena mengklaim mengenai teorema itu, ya. Ia mendapat penghargaan atas teorema ini karena dianggap telah menyebarkan pengetahuan tersebut ke peradaban Yunani, serta telah membuktikan rumusnya secara sistematis. Nah, sejak saat itulah pengetahuan menganai relasi antara sisi-sisi segitiga siku-siku dinamakan Teorema Pythagoras.
Konsep Rumus Teorema Pythagoras
Teorema Pythagoras adalah teorema yang menjelaskan hubungan panjang sisi pada segitiga siku-siku. Oleh karena itu, teorema ini hanya berlaku pada segitiga siku-siku aja. Kamu tau kan, segitiga siku-siku itu kayak gimana?
Eits, cara mengenali segitiga siku-siku itu gampang, kok. Salah satu cirinya adalah besar sudut sikunya ada yang 90o. Nah, sekarang, coba deh kamu lihat gambar segitiga siku-siku di bawah ini!
Segitiga siku-siku (sumber: id.wikipedia.co.id)
Misalkan ada segitiga siku-siku ABC, seperti pada gambar di atas. Sisi-sisi pada segitiga tersebut dinamai sesuai dengan nama sudut di depannya. Jadi, kalo sisi dari titik A ke B, bisa dinamai dengan c, karena sudut di depan sisi tersebut adalah ∠C . Hal yang harus kamu ingat, penamaan nama sisi itu harus pakai huruf kecil, ya.
Kemudian, sisi a dan b merupakan sisi tegak pada segitiga siku-siku. Kenapa disebut sisi tegak? Soalnya, kedua sisi tersebut membentuk sudut siku-siku (90o). Sementara itu, sisi c merupakan sisi miring (hipotenusa) segitiga siku-siku. Nah, sisi hipotenusa ini selalu berhadapan dengan sudut siku-sikunya, dan jadi sisi yang paling panjang, guys.
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Bunyi Teorema Pythagoras
Nah, Teorema Pythagoras menyatakan bahwa kuadrat panjang hipotenusa pada suatu segitiga siku-siku (salah satu sudutnya 90°) adalah sama dengan jumlah kuadrat panjang sisi-sisi lainnya. Atau, kalau mau dituliskan secara matematis, akan seperti ini:
Dengan c adalah hipotenusa yang juga merupakan sisi terpanjang dari segitiga siku-siku, sedangkan a dan b adalah sisi-sisi segitiga siku-siku lainnya. Gimana, sampai sini, apakah kamu mulai paham dengan rumus Teorema Pythagoras? Oke, supaya belajarnya lebih mantap lagi, kita coba kerjakan latihan soal di bawah ini, yuk!
Contoh Soal Teorema Pythagoras
Teorema Pythagoras ini bisa digunakan untuk mencari panjang sisi pada segitiga siku-siku yang belum diketahui, lho. Contohnya pada soal berikut!
Contoh Soal 1
1. Terdapat segitiga PQR siku-siku di Q. Jika diketahui panjang sisi PQ = 5cm dan QR = 12 cm, maka panjang sisi PR adalah…
Penyelesaian:
Supaya lebih mudah dalam menghitung, kita gambar dulu segitiga siku-sikunya, seperti ini:
Sehingga,
PQ2 + QR2 = PR2
52 + 122 = PR2
25 + 144 = PR2
169 = PR2
PR = ±√169
PR = ±13
Nah, karena PR itu panjang hipotenusa, yang artinya tidak boleh negatif, maka nilai PR yang memenuhi adalah 13 cm.
Contoh Soal 2
2. Segitiga siku-siku KLM, jika panjang KL = 2,5 m dan KM = 6,5 m, maka keliling segitiga KLM adalah …
Penyelesaian:
Keliling segitiga KLM bisa dicari dengan menjumlahkan ketiga sisinya. Berarti, kita cari terlebih dulu panjang sisi LM menggunakan Teorema Pythagoras.
KL2 + LM2 = KM2
LM2 = KM2 – KL2
LM2 = (6,5)2 – (2,5)2
LM2 = 42,25 – 6,25
LM2 = 36
LM = ±√36
LM = ± 6
Inget ya, kita pilih yang tandanya positif karena panjang sisi nggak mungkin negatif. Jadi, panjang sisi LM adalah 6 m. Sehingga, keliling segitiga KLM adalah,
Keliling segitiga KLM = KL + LM + KM = 2,5 + 6 + 6,5 = 15 m.
Baca Juga: Cara Menyelesaikan Bentuk-Bentuk Aljabar
Hubungan Teorema Pythagoras dengan Jenis Segitiga
Meskipun rumus Teorema Pythagoras hanya bisa digunakan untuk mencari sisi-sisi pada segitiga siku-siku, tapi kita juga bisa menggunakan teorema ini untuk mencari tahu bagaimana bentuk segitiga hanya dari nilai sisi-sisinya saja.
Misalkan, kita punya segitiga dengan a, b, dan c merupakan sisi-sisi segitiga tersebut. Maka sisi a, b, dan c dapat membentuk segitiga dengan tiga kemungkinan, di antaranya:
Jadi, dengan menggunakan Teorema Pythagoras, kita juga dapat menentukan, apakah ketiga barisan bilangan dapat membentuk segitiga siku-siku atau tidak. Contoh:
Diketahui sisi-sisi sebuah segitiga, yaitu a = 10, b = 8 dan c = 22. Dengan mengudaratkan sisi miring dan jumlahkan kuadrat sisi lainnya, maka diperoleh:
c2 = 222
c2 = 484
a2 + b2 = 102 + 82
a2 + b2 = 100 + 64
a2 + b2 = 164
Karena 164 < 484 atau a2 + b2 < c2 (102 + 82 < 222), maka segitiga ini bukan termasuk segitiga siku-siku, melainkan segitiga tumpul.
Apa itu Triple Pythagoras?
Setelah memahami isi dari Teorema Pythagoras, kita lanjut ke bahasan berikutnya, nih, yaitu Triple Pythagoras. Waduh, apa lagi, tuh? Triple Pythagoras adalah pasangan tiga bilangan asli yang memenuhi Teorema Pythagoras.
Beberapa pasangan 3 bilangan asli yang memenuhi Triple Pythagoras, di antaranya:
Triple Pythagoras ini bisa membantu kita untuk menentukan, mana kumpulan bilangan yang termasuk segitiga siku-siku dengan cara yang lebih cepat. Oke, supaya kamu nggak bingung, kita masuk ke contoh soalnya aja, ya.
Misalnya, diketahui segitiga dengan panjang sisi-sisinya, yaitu 6, 8, dan 10. Nah, menurutmu, apakah ketiga sisi tersebut merupakan triple Pythagoras?
Jawabannya, iya. Karena 6, 8, dan 10 merupakan kelipatan dari 3, 4, dan 5. Alhasil segitiga tersebut pasti merupakan segitiga siku-siku. Cepat kan ya?
Manfaat Teorema Pythagoras dalam Kehidupan Sehari-hari
Gunanya apa sih belajar Teorema Pythagoras? Tenang, setiap ilmu yang kamu pelajari, pasti ada manfaatnya, kok. Tidak ada yang sia-sia di dunia ini (ciee…).
Di jenjang SMA nanti, materi Teorema Pythagoras masih tetap dipelajari, sebagai dasar untuk mempelajari Trigonometri, yaitu salah satu cabang ilmu Matematika yang membahas hubungan antara panjang dan sudut segitiga. Sementara itu, di kehidupan sehari-hari, Teorema Pythagoras juga punya kegunaan yang cukup penting. Di antaranya:
1. Sistem Navigasi
Dalam sistem navigasi, ada yang namanya metode triangulasi yang digunakan untuk menentukan lokasi atau koordinat berdasarkan sudut antar titik koordinatnya. Nah, Teorema Pythagoras dapat dimanfaatkan ketika triangulasi menggunakan sudut 90.
Sementara itu, para pelaut menggunakan teorema ini untuk menghitung rute terpendek dengan menggambar dua garis vertikal dan dua garis horizontal dari posisi kapal, pilot menggunakan teorema ini untuk menentukan geolokasi yang tepat untuk memulai penurunan yang aman menuju bandara tujuan, dan kita bisa menggunakan Teorema Pythagoras untuk sistem navigasi mobil atau pelacakan ponsel.
2. Arsitektur dan Konstruksi
Dalam bidang arsitektur dan konstruksi, Teorema Pythagoras bisa diaplikasikan, khususnya pada bangunan atau bidang yang berbentuk segitiga. Contohnya, atap bangunan. Rumus dasar teorema Pythagoras, yang menyatakan bahwa sebuah segitiga akan selalu memiliki sudut tegak jika sisi-sisinya memenuhi kondisi tertentu, digunakan oleh para insinyur dalam membuat kerangka bangunan ini.
3. Desain Layar Televisi atau Monitor
Kamu tahu nggak, ukuran TV dan monitor selalu ditentukan dalam satuan diagonal, loh. Misalnya, jika sebuah televisi memiliki ukuran 32 inci, maka ukuran keseluruhannya dilakukan menggunakan pengukuran diagonal, yang dikenal sebagai sisi miring (hipotenusa). Jadi, dengan kata lain, Teorema Pythagoras juga bermanfaat dalam membantu mengukur layar TV, monitor, atau bahkan layar HP kamu.
Nah, selain manfaat di atas, Teorema Pythagoras juga merupakan dasar untuk banyak bidang di luar matematika, mulai dari fisika, geologi, arsitektur, dan lainnya.
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Ternyata, mudah ya cara menentukan panjang sisi-sisi pada segitiga siku-siku dengan menggunakan Teorema Pythagoras itu. Kalau kamu punya cara lain yang diajarkan sekolahmu, boleh juga di-share di kolom komentar supaya yang lain tahu!
Tentunya, kamu dapat memelajari materi seperti ini dengan cara yang lebih asyik. Seperti menonton video beranimasi dari ruangbelajar, misalnya. Di sana, kamu akan mendapatkan rangkuman dan latihan-latihan soal yang membantumu memahami lebih dalam tentang pelajaran sekolah, lho!
Referensi:
Raharjo M, Setiawan A. (2018) Matematika SMP/MTs Kelas VIII. Jakarta: Erlangga
Sumber foto:
Ilustrasi ‘Segitiga Siku-Siku’ [Daring]. Tautan: https://id.wikipedia.org/wiki/Segitiga_siku-siku (Diakses: 21 Januari 2022)
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<h1 class="content-title">
Rumus Teorema Pythagoras, Sejarah & Contoh Soal | Matematika Kelas 8 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/hani-ammariah" class="">Hani Ammariah</a> </p>
<p class="content-info"><span>September 3, 2025 • </span> <span>7 minutes read</span></p>
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<p style="text-align: justify;"><img decoding="async" style="width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/MAT08%20-%20Teorema%20Pythagoras-01.jpg" alt="Teorema Pythagoras" /></p>
<blockquote>
<p style="text-align: center;"><em>Ayo, kita belajar bersama-sama materi tentang rumus Teorema Pythagoras, cara menghitungnya dengan mudah, hingga sejarahnya di <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-8">artikel Matematika kelas 8</a></strong> ini!</em></p>
</blockquote>
<p style="text-align: center;">—</p>
<p> </p>
<p style="text-align: justify;">Apakah kamu pernah mendengar Pythagoras? Ia merupakan seorang matematikawan dan filsuf Yunani yang dikenal sebagai “Bapak Bilangan”. Salah satu peninggalannya yang bersejarah, yaitu Teorema Pythagoras! <span style="color: #000000;"><br />
</span></p>
<p style="text-align: justify;">Di artikel kali ini, kita akan belajar sama-sama mengenai Teorema Pythagoras. Apa sih Teorema Pythagoras itu? Dari mana asal-usul rumus Teorema Pythagoras? Seperti apa ya cara menghitungnya? Nah, langsung aja simak pembahasan berikut ini, ya!</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Sejarah di Balik Teorema Pythagoras</span></h2>
<p style="text-align: justify;">Layaknya Hukum Newton yang ditemukan oleh Sir Isaac Newton, atau Hukum Archimedes yang ditemukan oleh Archimedes, kebanyakan dari kamu mungkin mengira kalau Teorema Pythagoras juga ditemukan oleh Bapak Bilangan satu ini, deh.</p>
<p style="text-align: justify;">Nyatanya, <strong>Pythagoras bukanlah penemu pertama dari teorema ini</strong>, loh! Loh, kok? Kenapa bisa ya, bukan orang yang menemukan, tapi namanyalah yang digunakan untuk teorema ini? Mari kita simak sejarahnya, <em>guys</em>!</p>
<p style="text-align: justify;">Sebenarnya, <strong>Teorema Pythagoras sudah digunakan sejak lama</strong>, yaitu sekitar abad ke 1900 – 1600 SM oleh bangsa Mesir, Babilonia, dan Cina Kuno. Mereka sudah memiliki pemahaman mengenai relasi (hubungan) antara sisi-sisi segitiga siku-siku, <strong>jauh sebelum Pythagoras lahir</strong>.</p>
<p style="text-align: justify;">Salah satu bukti sejarahnya, yakni penemuan <strong>tablet milik peradaban bangsa Babilonia</strong>. Pada tablet tersebut, tertulis banyak <strong>kombinasi 3 angka yang memenuhi syarat Teorema Pythagoras</strong>. Kalau sekarang sih, kita menyebutnya dengan Triple Pythagoras. Diperkirakan bahwa pengetahuan inilah yang mendasari bangsa peradaban kuno untuk membangun piramida.</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/e4b4dd4b-1fd8-42e8-a4cb-4a57005429c6.png" alt="tablet babilonia - teorema pythagoras" /></p>
<p> </p>
<p style="text-align: justify;">Namun, Pythagoras juga tidak semena-mena mengklaim mengenai teorema itu, ya. Ia mendapat penghargaan atas teorema ini karena dianggap telah <strong>menyebarkan pengetahuan tersebut ke peradaban Yunani</strong>, serta telah <strong>membuktikan rumusnya secara sistematis</strong>. Nah, sejak saat itulah pengetahuan menganai relasi antara sisi-sisi segitiga siku-siku dinamakan Teorema Pythagoras.</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;"><strong>Konsep Rumus Teorema Pythagoras</strong></span></h2>
<p style="text-align: justify;"><strong>Teorema Pythagoras adalah teorema yang menjelaskan hubungan panjang sisi pada segitiga siku-siku</strong>. Oleh karena itu, teorema ini hanya berlaku pada segitiga siku-siku aja. Kamu tau kan, segitiga siku-siku itu kayak gimana?</p>
<p style="text-align: justify;">Eits, cara mengenali segitiga siku-siku itu gampang, kok. Salah satu cirinya adalah besar sudut sikunya ada yang 90<sup>o</sup>. Nah, sekarang, coba deh kamu lihat gambar segitiga siku-siku di bawah ini!</p>
<p style="text-align: center;"><img decoding="async" style="width: 220px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/segitiga%20siku-siku-1.png" alt="segitiga siku-siku-1" width="220" /><em>Segitiga siku-siku (sumber: id.wikipedia.co.id)</em></p>
<p> </p>
<p style="text-align: justify;">Misalkan ada segitiga siku-siku ABC, seperti pada gambar di atas. Sisi-sisi pada segitiga tersebut dinamai sesuai dengan nama sudut di depannya. Jadi, kalo sisi dari titik A ke B, bisa dinamai dengan c, karena sudut di depan sisi tersebut adalah ∠C . Hal yang harus kamu ingat, penamaan nama sisi itu harus pakai huruf kecil, ya.</p>
<p style="text-align: justify;">Kemudian, <strong>sisi a dan b merupakan sisi tegak</strong> pada segitiga siku-siku. Kenapa disebut sisi tegak? Soalnya, kedua sisi tersebut membentuk sudut siku-siku (90<sup>o</sup>). Sementara itu, <strong>sisi c merupakan</strong> <strong>sisi miring (hipotenusa)</strong> segitiga siku-siku. Nah, sisi hipotenusa ini selalu berhadapan dengan sudut siku-sikunya, dan jadi sisi yang paling panjang, guys.</p>
<p style="text-align: justify; font-weight: bold;">Baca Juga: <a href="/blog/jenis-jenis-bilangan-pecahan" rel="noopener">Jenis-Jenis Bilangan Pecahan dan Contohnya</a></p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Bunyi Teorema Pythagoras</span></h2>
<p style="text-align: justify;">Nah, Teorema Pythagoras menyatakan bahwa <strong>kuadrat panjang hipotenusa pada suatu segitiga siku-siku (salah satu sudutnya 90°) adalah sama dengan jumlah kuadrat panjang sisi-sisi lainnya</strong>. Atau, kalau mau dituliskan secara matematis, akan seperti ini:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/MAT08%20-%20Teorema%20Pythagoras-03%20(1).jpg" alt="Teorema Pythagoras" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Dengan c adalah hipotenusa yang juga merupakan sisi terpanjang dari segitiga siku-siku, sedangkan a dan b adalah sisi-sisi segitiga siku-siku lainnya. Gimana, sampai sini, apakah kamu mulai paham dengan rumus Teorema Pythagoras? Oke, supaya belajarnya lebih mantap lagi, kita coba kerjakan latihan soal di bawah ini, yuk!</p>
<p> </p>
<h2 style="font-size: 20px; text-align: justify;"><span style="font-size: 18pt;">Contoh Soal Teorema Pythagoras</span></h2>
<p style="text-align: justify;">Teorema Pythagoras ini bisa digunakan untuk mencari panjang sisi pada segitiga siku-siku yang belum diketahui, lho. Contohnya pada soal berikut!</p>
<p> </p>
<p style="text-align: justify;"><strong>Contoh Soal 1</strong></p>
<p style="text-align: justify;">1. Terdapat segitiga PQR siku-siku di Q. Jika diketahui panjang sisi PQ = 5cm dan QR = 12 cm, maka panjang sisi PR adalah…</p>
<p style="font-weight: bold; text-align: justify;">Penyelesaian:</p>
<p style="line-height: 1em; text-align: justify;">Supaya lebih mudah dalam menghitung, kita gambar dulu segitiga siku-sikunya, seperti ini:</p>
<p style="line-height: 1em; text-align: justify;"><img decoding="async" style="width: 200px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/segitiga%20siku-siku%20PQR.png" alt="segitiga siku-siku PQR" width="200" /></p>
<p> </p>
<p style="line-height: 1em; text-align: justify;">Sehingga,</p>
<p style="line-height: 1em; text-align: justify;"><em>PQ<sup>2</sup> + QR<sup>2</sup> = PR<sup>2</sup></em></p>
<p style="line-height: 1em; text-align: justify;"><em>5<sup>2</sup> + 12<sup>2 </sup>= PR<sup>2</sup></em></p>
<p style="line-height: 1em; text-align: justify;"><em>25 + 144 = PR<sup>2</sup></em></p>
<p style="line-height: 1em; text-align: justify;"><em>169 = PR<sup>2</sup></em></p>
<p style="line-height: 1em; text-align: justify;"><em>PR = ±√169</em></p>
<p style="line-height: 1em; text-align: justify;"><em>PR</em> = <em>±</em>13</p>
<p> </p>
<p style="text-align: justify;">Nah, karena PR itu panjang hipotenusa, yang artinya tidak boleh negatif, maka nilai PR yang memenuhi adalah 13 cm.</p>
<p> </p>
<p style="text-align: justify;"><strong>Contoh Soal 2</strong></p>
<p style="text-align: justify;">2. Segitiga siku-siku KLM, jika panjang KL = 2,5 m dan KM = 6,5 m, maka keliling segitiga KLM adalah …</p>
<p style="font-weight: bold; text-align: justify;">Penyelesaian:</p>
<p style="font-weight: normal; text-align: justify;">Keliling segitiga KLM bisa dicari dengan menjumlahkan ketiga sisinya. Berarti, kita cari terlebih dulu panjang sisi LM menggunakan Teorema Pythagoras.</p>
<p style="font-weight: normal; text-align: justify;"><img decoding="async" style="width: 200px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/segitiga%20siku-siku%20KLM.png" alt="segitiga siku-siku KLM" width="200" /></p>
<p> </p>
<p style="font-weight: normal; text-align: justify;"><em>KL<sup>2</sup> + LM<sup>2</sup> = KM<sup>2</sup></em></p>
<p style="font-weight: normal; text-align: justify;"><em>LM<sup>2</sup> = KM<sup>2 </sup>– KL<sup>2</sup></em></p>
<p style="font-weight: normal; text-align: justify;"><em>LM<sup>2</sup> = (6,5)<sup>2 </sup>– (2,5)<sup>2</sup></em></p>
<p style="font-weight: normal; text-align: justify;"><em>LM<sup>2</sup> = 42,25 – 6,25</em></p>
<p style="font-weight: normal; text-align: justify;"><em>LM<sup>2</sup> = 36</em></p>
<p style="line-height: 1em; text-align: justify;"><em>LM = ±√36</em></p>
<p style="line-height: 1em; text-align: justify;"><em>LM</em> = <em>± </em>6</p>
<p> </p>
<p style="text-align: justify;">Inget ya, kita pilih yang tandanya positif karena panjang sisi nggak mungkin negatif. Jadi, panjang sisi LM adalah 6 m. Sehingga, keliling segitiga KLM adalah,</p>
<p style="line-height: 1em; text-align: justify;">Keliling segitiga KLM = KL + LM + KM = 2,5 + 6 + 6,5 = 15 m.</p>
<p style="line-height: 1em; font-weight: bold; text-align: justify;">Baca Juga: <a href="/blog/penyelesaian-bentuk-bentuk-aljabar" rel="noopener">Cara Menyelesaikan Bentuk-Bentuk Aljabar</a></p>
<p> </p>
<h2 style="font-size: 20px; font-weight: bold; text-align: justify;"><span style="font-size: 18pt;">Hubungan Teorema Pythagoras dengan Jenis Segitiga</span></h2>
<p style="font-weight: normal; text-align: justify;">Meskipun rumus Teorema Pythagoras hanya bisa digunakan untuk mencari sisi-sisi pada segitiga siku-siku, tapi kita juga bisa menggunakan teorema ini untuk mencari tahu bagaimana bentuk segitiga hanya dari nilai sisi-sisinya saja.</p>
<p style="font-weight: normal; text-align: justify;">Misalkan, kita punya segitiga dengan a, b, dan c merupakan sisi-sisi segitiga tersebut. Maka sisi a, b, dan c dapat membentuk segitiga dengan tiga kemungkinan, di antaranya:</p>
<p style="font-weight: normal; text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/MAT08%20-%20Teorema%20Pythagoras-04%20(2).jpg" alt="hubungan teorema pythagoras" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Jadi, dengan menggunakan Teorema Pythagoras, kita juga dapat menentukan, <strong>apakah ketiga barisan bilangan dapat membentuk segitiga siku-siku atau tidak</strong>. Contoh:</p>
<p style="text-align: justify;">Diketahui sisi-sisi sebuah segitiga, yaitu a = 10, b = 8 dan c = 22. Dengan mengudaratkan sisi miring dan jumlahkan kuadrat sisi lainnya, maka diperoleh:</p>
<p style="line-height: 1em; text-align: justify;"><em>c<sup>2</sup></em> = 22<sup>2</sup></p>
<p style="line-height: 1em; text-align: justify;"><em>c</em><sup>2</sup> = 484</p>
<p style="line-height: 1em; text-align: justify;"><em>a</em><sup>2</sup> + <em>b<sup>2</sup></em> = 10<sup>2</sup> + 8<sup>2</sup></p>
<p style="line-height: 1em; text-align: justify;"><em>a</em><sup>2</sup> + <em>b<sup>2</sup></em> = 100 + 64</p>
<p style="line-height: 1em; text-align: justify;"><em>a</em><sup>2</sup> + <em>b<sup>2</sup></em> = 164</p>
<p> </p>
<p style="text-align: justify;">Karena 164 < 484 atau a<sup>2 </sup>+ b<sup>2 </sup>< c<sup>2</sup> (10<sup>2</sup> + 8<sup>2</sup> < 22<sup>2</sup>), maka segitiga ini <span style="font-weight: bold;">bukan termasuk segitiga siku-siku, melainkan segitiga tumpul</span>.</p>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px; text-align: justify;"><span style="font-size: 18pt;">Apa itu Triple Pythagoras?</span></h2>
<p style="text-align: justify;">Setelah memahami isi dari Teorema Pythagoras, kita lanjut ke bahasan berikutnya, nih, yaitu Triple Pythagoras. Waduh, apa lagi, tuh? <strong>Triple Pythagoras adalah pasangan tiga bilangan asli yang memenuhi Teorema Pythagoras</strong>.</p>
<p style="text-align: justify;">Beberapa pasangan 3 bilangan asli yang memenuhi Triple Pythagoras, di antaranya:</p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/MAT08%20-%20Teorema%20Pythagoras-05.jpg" alt="Triple Pythagoras" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Triple Pythagoras ini bisa membantu kita untuk <strong>menentukan, mana kumpulan bilangan yang termasuk segitiga siku-siku dengan cara yang lebih cepat</strong>. Oke, supaya kamu nggak bingung, kita masuk ke contoh soalnya aja, ya.</p>
<p style="text-align: justify;">Misalnya, diketahui segitiga dengan panjang sisi-sisinya, yaitu 6, 8, dan 10. Nah, menurutmu, apakah ketiga sisi tersebut merupakan triple Pythagoras?</p>
<p style="text-align: justify;">Jawabannya, iya. Karena 6, 8, dan 10 merupakan kelipatan dari 3, 4, dan 5. Alhasil segitiga tersebut pasti merupakan segitiga siku-siku. Cepat kan ya?</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Manfaat Teorema Pythagoras dalam Kehidupan Sehari-hari</span></h2>
<p style="text-align: justify;">Gunanya apa sih belajar Teorema Pythagoras? Tenang, setiap ilmu yang kamu pelajari, pasti ada manfaatnya, kok. Tidak ada yang sia-sia di dunia ini (ciee…).</p>
<p style="text-align: justify;">Di jenjang SMA nanti, materi Teorema Pythagoras masih tetap dipelajari, sebagai dasar untuk mempelajari Trigonometri, yaitu salah satu cabang ilmu Matematika yang membahas hubungan antara panjang dan sudut segitiga. Sementara itu, di kehidupan sehari-hari, Teorema Pythagoras juga punya kegunaan yang cukup penting. Di antaranya:</p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">1. Sistem Navigasi</span></h3>
<p style="text-align: justify;">Dalam sistem navigasi, ada yang namanya metode triangulasi yang digunakan untuk menentukan lokasi atau koordinat berdasarkan sudut antar titik koordinatnya. Nah, Teorema Pythagoras dapat dimanfaatkan ketika triangulasi menggunakan sudut 90.</p>
<p style="text-align: justify;">Sementara itu, para pelaut menggunakan teorema ini untuk menghitung rute terpendek dengan menggambar dua garis vertikal dan dua garis horizontal dari posisi kapal, pilot menggunakan teorema ini untuk menentukan geolokasi yang tepat untuk memulai penurunan yang aman menuju bandara tujuan, dan kita bisa menggunakan Teorema Pythagoras untuk sistem navigasi mobil atau pelacakan ponsel.</p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">2. Arsitektur dan Konstruksi</span></h3>
<p style="text-align: justify;">Dalam bidang arsitektur dan konstruksi, Teorema Pythagoras bisa diaplikasikan, khususnya pada bangunan atau bidang yang berbentuk segitiga. Contohnya, atap bangunan. Rumus dasar teorema Pythagoras, yang menyatakan bahwa sebuah segitiga akan selalu memiliki sudut tegak jika sisi-sisinya memenuhi kondisi tertentu, digunakan oleh para insinyur dalam membuat kerangka bangunan ini.</p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">3. Desain Layar Televisi atau Monitor</span></h3>
<p style="text-align: justify;">Kamu tahu nggak, ukuran TV dan monitor selalu ditentukan dalam satuan diagonal, loh. Misalnya, jika sebuah televisi memiliki ukuran 32 inci, maka ukuran keseluruhannya dilakukan menggunakan pengukuran diagonal, yang dikenal sebagai sisi miring (hipotenusa). Jadi, dengan kata lain, Teorema Pythagoras juga bermanfaat dalam membantu mengukur layar TV, monitor, atau bahkan layar HP kamu.</p>
<p style="text-align: justify;">Nah, selain manfaat di atas, Teorema Pythagoras juga merupakan dasar untuk banyak bidang di luar matematika, mulai dari fisika, geologi, arsitektur, dan lainnya.</p>
<p style="font-weight: bold; text-align: justify;">Baca Juga: <a href="/blog/pengertian-dan-rumus-menghitung-bruto-netto-dan-tara" rel="noopener">Pengertian dan Cara Menghitung Bruto, Netto, dan Tara</a></p>
<p style="text-align: justify;">Ternyata, mudah ya cara menentukan panjang sisi-sisi pada segitiga siku-siku dengan menggunakan Teorema Pythagoras itu. Kalau kamu punya cara lain yang diajarkan sekolahmu, boleh juga di-<em>share</em> di kolom komentar supaya yang lain tahu!</p>
<p style="text-align: justify;">Tentunya, kamu dapat memelajari materi seperti ini dengan cara yang lebih asyik. Seperti menonton video beranimasi dari <a href="https://ruangguru.com/belajar?utm_medium=referral&utm_source=blog&utm_campaign=bagaimana-cara-menghitung-teorema-pythagoras" target="_blank" rel="noopener"><strong>ruangbelajar</strong>,</a> misalnya. Di sana, kamu akan mendapatkan rangkuman dan latihan-latihan soal yang membantumu memahami lebih dalam tentang pelajaran sekolah, <em>lho!</em></p>
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<p style="text-align: justify;"><strong>Referensi:</strong></p>
<p style="text-align: justify;">Raharjo M, Setiawan A. (2018) Matematika SMP/MTs Kelas VIII. Jakarta: Erlangga</p>
<p style="text-align: justify;"><strong>Sumber foto:</strong></p>
<p style="text-align: justify;">Ilustrasi ‘Segitiga Siku-Siku’ [Daring]. Tautan: https://id.wikipedia.org/wiki/Segitiga_siku-siku (Diakses: 21 Januari 2022)</p>
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<p class="title">Hubungi Kami</p>
<address>
<a href="mailto:info@ruangguru.com">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4739a139-8f09-42ea-b517-d842c5d1c28d.png" loading="lazy" alt="Logo Email Footer" />
info@ruangguru.com</a>
<a href="tel:02130930000">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/6f4bb6c8-52c9-4acb-859b-47a10a7eec75.png" loading="lazy" alt="Logo Phone Footer" />(021) 3093 0000</a>
<a href="https://wa.me/6281574410000">
<img class="icon-call-us" src="https://cdn-web-2.ruangguru.com/file-uploader/lp/4b58468a-b2f9-40e4-867f-d3242a065dcf.png" loading="lazy" alt="Logo Whatsapp Footer" />0815 7441 0000</a>
</address>
</nav>
<nav class="footer-menu social d-none d-lg-block">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<div class="col-lg-9">
<div class="row">
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
<li><a href="https://www.ruangguru.com/dafa-lulu">Dafa dan Lulu</a></li>
<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
<li><a href="https://www.ruangguru.com/for-kids">Ruangguru for Kids</a></li>
<li><a href="https://www.ruangguru.com/bisnis">Ruangguru for Business</a></li>
<li><a href="https://www.ruangguru.com/ruanguji">Ruanguji</a></li>
<li><a href="https://www.ruangguru.com/blog">Ruangbaca</a></li>
<li><a href="https://www.ruangguru.com/ruangkelas">Ruangkelas</a></li>
<li><a href="https://www.ruangguru.com/ruangbelajar">Ruangbelajar</a></li>
<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
<li><a href="https://www.english-academy.id/" target="_blank">English Academy</a></li>
<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>