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2026-01-01
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2026-02-28
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<p>119 Learners</p>
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<p>Last updated on<strong>September 25, 2025</strong></p>
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<p>Last updated on<strong>September 25, 2025</strong></p>
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<p>In geometry, understanding the relationships between the sides of a triangle is crucial. The Pythagorean theorem, the Law of Sines, and the Law of Cosines are key formulas that relate the sides and angles of triangles. In this topic, we will learn the formulas for these fundamental relationships.</p>
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<p>In geometry, understanding the relationships between the sides of a triangle is crucial. The Pythagorean theorem, the Law of Sines, and the Law of Cosines are key formulas that relate the sides and angles of triangles. In this topic, we will learn the formulas for these fundamental relationships.</p>
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<h2>List of Math Formulas for the Sides of a Triangle</h2>
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<h2>List of Math Formulas for the Sides of a Triangle</h2>
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<p>The relationships between the sides and angles<a>of</a>triangles are expressed through the Pythagorean theorem, the Law of Sines, and the Law of Cosines.</p>
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<p>The relationships between the sides and angles<a>of</a>triangles are expressed through the Pythagorean theorem, the Law of Sines, and the Law of Cosines.</p>
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<p>Let’s learn the<a>formulas</a>to calculate the sides of a triangle.</p>
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<p>Let’s learn the<a>formulas</a>to calculate the sides of a triangle.</p>
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<h2>Pythagorean Theorem</h2>
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<h2>Pythagorean Theorem</h2>
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<p>The Pythagorean theorem applies to right-angled triangles. It is expressed as: a2 + b2 = c2 where c is the hypotenuse, and a and b are the other two sides.</p>
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<p>The Pythagorean theorem applies to right-angled triangles. It is expressed as: a2 + b2 = c2 where c is the hypotenuse, and a and b are the other two sides.</p>
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<h2>Law of Sines</h2>
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<h2>Law of Sines</h2>
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<p>The Law of Sines relates the sides of a triangle to its angles. It is expressed as: a/sin A = b/sin B =c/sin C where a, b, c are the sides and A, B, C are the opposite angles.</p>
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<p>The Law of Sines relates the sides of a triangle to its angles. It is expressed as: a/sin A = b/sin B =c/sin C where a, b, c are the sides and A, B, C are the opposite angles.</p>
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<h3>Explore Our Programs</h3>
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<h3>Explore Our Programs</h3>
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<p>No Courses Available</p>
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<h2>Law of Cosines</h2>
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<h2>Law of Cosines</h2>
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<p>The Law of Cosines is useful for calculating an unknown side or angle in any triangle. It is expressed as: c2 = a2 + b2- 2abcos C where c is the side opposite angle C .</p>
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<p>The Law of Cosines is useful for calculating an unknown side or angle in any triangle. It is expressed as: c2 = a2 + b2- 2abcos C where c is the side opposite angle C .</p>
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<h2>Importance of Triangle Side Formulas</h2>
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<h2>Importance of Triangle Side Formulas</h2>
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<p>Triangle side formulas are fundamental in<a>geometry</a>and real-world applications. Here are some important points about these formulas:</p>
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<p>Triangle side formulas are fundamental in<a>geometry</a>and real-world applications. Here are some important points about these formulas:</p>
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<ol><li>They help in solving geometry problems involving triangles. </li>
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<ol><li>They help in solving geometry problems involving triangles. </li>
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<li>The formulas are essential in fields like architecture, navigation, and physics. </li>
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<li>The formulas are essential in fields like architecture, navigation, and physics. </li>
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<li>Understanding these formulas aids in grasping more complex mathematical concepts.</li>
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<li>Understanding these formulas aids in grasping more complex mathematical concepts.</li>
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</ol><h2>Tips and Tricks to Memorize Triangle Side Formulas</h2>
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</ol><h2>Tips and Tricks to Memorize Triangle Side Formulas</h2>
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<p>Students often find triangle formulas challenging. Here are some tips to master them: </p>
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<p>Students often find triangle formulas challenging. Here are some tips to master them: </p>
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<ul><li>Use mnemonics or visual aids to remember the Pythagorean theorem and laws of sines and cosines.</li>
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<ul><li>Use mnemonics or visual aids to remember the Pythagorean theorem and laws of sines and cosines.</li>
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</ul><ul><li>Practice with different triangle problems to build familiarity. </li>
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</ul><ul><li>Practice with different triangle problems to build familiarity. </li>
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</ul><ul><li>Create a formula sheet for quick reference and revise it regularly.</li>
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</ul><ul><li>Create a formula sheet for quick reference and revise it regularly.</li>
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</ul><h2>Common Mistakes and How to Avoid Them While Using Triangle Side Formulas</h2>
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</ul><h2>Common Mistakes and How to Avoid Them While Using Triangle Side Formulas</h2>
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<p>Students make errors when applying triangle formulas. Here are some mistakes and how to avoid them:</p>
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<p>Students make errors when applying triangle formulas. Here are some mistakes and how to avoid them:</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Find the hypotenuse of a right triangle with sides 3 and 4.</p>
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<p>Find the hypotenuse of a right triangle with sides 3 and 4.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The hypotenuse is 5.</p>
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<p>The hypotenuse is 5.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the Pythagorean theorem: a2 + b2 = c2 </p>
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<p>Using the Pythagorean theorem: a2 + b2 = c2 </p>
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<p>32 + 42 = c2</p>
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<p>32 + 42 = c2</p>
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<p>9 + 16 = c2</p>
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<p>9 + 16 = c2</p>
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<p>25 = c2 </p>
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<p>25 = c2 </p>
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<p>c = 5 </p>
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<p>c = 5 </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>In a triangle with sides 7, 9, and angle 45° opposite the side 7, find the third side using the Law of Cosines.</p>
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<p>In a triangle with sides 7, 9, and angle 45° opposite the side 7, find the third side using the Law of Cosines.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The third side is approximately 5.2.</p>
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<p>The third side is approximately 5.2.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the Law of Cosines: c2 = a2 + b2 - 2abcos C </p>
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<p>Using the Law of Cosines: c2 = a2 + b2 - 2abcos C </p>
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<p>c2 = 72 + 92 - 2 x 7 x 9 x cos 45°</p>
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<p>c2 = 72 + 92 - 2 x 7 x 9 x cos 45°</p>
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<p>c2 = 49 + 81 - 126 x 0.7071 </p>
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<p>c2 = 49 + 81 - 126 x 0.7071 </p>
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<p>c2 = 130 - 89.131 </p>
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<p>c2 = 130 - 89.131 </p>
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<p>c2 = 40.869</p>
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<p>c2 = 40.869</p>
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<p>c ≈ 6.39</p>
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<p>c ≈ 6.39</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>In a triangle with angles 30°, 60°, and 90°, and the hypotenuse is 10, find the side opposite the 30° angle.</p>
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<p>In a triangle with angles 30°, 60°, and 90°, and the hypotenuse is 10, find the side opposite the 30° angle.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The side opposite the 30° angle is 5.</p>
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<p>The side opposite the 30° angle is 5.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the property of 30-60-90 triangles, the side opposite the 30° angle is half the hypotenuse. Therefore, it is 10/2 = 5.</p>
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<p>Using the property of 30-60-90 triangles, the side opposite the 30° angle is half the hypotenuse. Therefore, it is 10/2 = 5.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>A triangle has sides 5, 12, and angle 90° opposite the side 5. Find the third side.</p>
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<p>A triangle has sides 5, 12, and angle 90° opposite the side 5. Find the third side.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The third side is 13.</p>
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<p>The third side is 13.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the Pythagorean theorem: a2 + b2 = c2 </p>
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<p>Using the Pythagorean theorem: a2 + b2 = c2 </p>
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<p>52 + 122 = c2</p>
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<p>52 + 122 = c2</p>
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<p>25 + 144 = c2</p>
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<p>25 + 144 = c2</p>
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<p>169 = c2</p>
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<p>169 = c2</p>
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<p>c = 13</p>
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<p>c = 13</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Given a triangle with sides 8, 15, and angle 60° opposite the side 8, find the third side using the Law of Cosines.</p>
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<p>Given a triangle with sides 8, 15, and angle 60° opposite the side 8, find the third side using the Law of Cosines.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The third side is approximately 13.9.</p>
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<p>The third side is approximately 13.9.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Using the Law of Cosines:c2= a2 + b2 - 2abcos C </p>
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<p>Using the Law of Cosines:c2= a2 + b2 - 2abcos C </p>
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<p>c2 = 82 + 152 - 2 x 8 x 15 x cos 60° \</p>
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<p>c2 = 82 + 152 - 2 x 8 x 15 x cos 60° \</p>
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<p>c2 = 64 + 225 - 240 x 0.5 </p>
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<p>c2 = 64 + 225 - 240 x 0.5 </p>
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<p>c2 = 289 - 120 </p>
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<p>c2 = 289 - 120 </p>
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<p>c2= 169 </p>
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<p>c2= 169 </p>
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<p>c = 13 </p>
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<p>c = 13 </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Triangle Side Formulas</h2>
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<h2>FAQs on Triangle Side Formulas</h2>
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<h3>1.What is the Pythagorean theorem?</h3>
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<h3>1.What is the Pythagorean theorem?</h3>
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<p>The Pythagorean theorem is: \( a^2 + b^2 = c^2 \) for right-angled triangles.</p>
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<p>The Pythagorean theorem is: \( a^2 + b^2 = c^2 \) for right-angled triangles.</p>
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<h3>2.What is the Law of Sines?</h3>
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<h3>2.What is the Law of Sines?</h3>
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<p>The Law of Sines is: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \).</p>
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<p>The Law of Sines is: \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \).</p>
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<h3>3.How to use the Law of Cosines?</h3>
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<h3>3.How to use the Law of Cosines?</h3>
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<p>To use the Law of Cosines, apply: \( c^2 = a^2 + b^2 - 2ab\cos C \).</p>
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<p>To use the Law of Cosines, apply: \( c^2 = a^2 + b^2 - 2ab\cos C \).</p>
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<h3>4.How do you find a missing side in a right triangle?</h3>
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<h3>4.How do you find a missing side in a right triangle?</h3>
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<p>In a right triangle, use the Pythagorean theorem to find the missing side.</p>
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<p>In a right triangle, use the Pythagorean theorem to find the missing side.</p>
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<h3>5.What is the relation between angles and sides in triangles?</h3>
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<h3>5.What is the relation between angles and sides in triangles?</h3>
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<p>The angles and sides of triangles are related through trigonometric functions and laws like Sines and Cosines.</p>
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<p>The angles and sides of triangles are related through trigonometric functions and laws like Sines and Cosines.</p>
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<h2>Glossary for Triangle Side Formulas</h2>
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<h2>Glossary for Triangle Side Formulas</h2>
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<ul><li><strong>Pythagorean Theorem:</strong>A formula used to find the sides of right-angled triangles, expressed as \( a^2 + b^2 = c^2 \).</li>
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<ul><li><strong>Pythagorean Theorem:</strong>A formula used to find the sides of right-angled triangles, expressed as \( a^2 + b^2 = c^2 \).</li>
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</ul><ul><li><strong>Law of Sines:</strong>A formula relating the sides and angles of a triangle, expressed as a/sin A = b/sin B = c/sin C.</li>
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</ul><ul><li><strong>Law of Sines:</strong>A formula relating the sides and angles of a triangle, expressed as a/sin A = b/sin B = c/sin C.</li>
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</ul><ul><li><strong>Law of Cosines:</strong>A formula to find an unknown side or angle in any triangle, expressed as c2 = a2 + b2 - 2abcos C.</li>
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</ul><ul><li><strong>Law of Cosines:</strong>A formula to find an unknown side or angle in any triangle, expressed as c2 = a2 + b2 - 2abcos C.</li>
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</ul><ul><li><strong>Hypotenuse:</strong>The longest side of a right-angled triangle, opposite the right angle.</li>
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</ul><ul><li><strong>Hypotenuse:</strong>The longest side of a right-angled triangle, opposite the right angle.</li>
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</ul><ul><li><strong>Trigonometric Functions:</strong>Functions like sine, cosine, and tangent used to relate angles and sides in triangles.</li>
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</ul><ul><li><strong>Trigonometric Functions:</strong>Functions like sine, cosine, and tangent used to relate angles and sides in triangles.</li>
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</ul><h2>Jaskaran Singh Saluja</h2>
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</ul><h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>