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The Pythagorean Theorem

Learn how to apply the Pythagorean Theorem to find hypotenuse lengths and triangle types in this lesson. Practice solving triangle problems step by step.

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The Pythagorean Theorem

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  1. a2 + b2 = c2Use the Pythagorean Theorem. 62 + 82 = c2Substitute a = 6, b = 8. 36 + 64 = c2Simplify. 100 = c2Add. 100 = c2Find the positive square root of each side. 10 = cSimplify. COURSE 3 LESSON 4-9 The Pythagorean Theorem Find the length of the hypotenuse of a right triangle whose legs are 6 ft and 8 ft. The length of the hypotenuse is 10 ft. 4-9

  2. The diagram shows a right triangle with hypotenuse 10 ft and leg 2.5 ft. The distance from the top of the ladder to the ground is a. COURSE 3 LESSON 4-9 The Pythagorean Theorem The bottom of a 10-foot ladder is 2.5 ft from the side of a wall. How far, to the nearest tenth, is the top of the ladder from the ground? 4-9

  3. a2 + b2 = c2 Use the Pythagorean Theorem. a2 + (2.5)2 = 102 Substitute b = 2.5 and c = 10. a2 + 6.25 = 100 Multiply. a2 = 93.75 Subtract 6.25 from each side. a = 93.75 Find the positive square root. 93.75 9.6824584 Use a calculator. a 9.7 Round to the nearest tenth. COURSE 3 LESSON 4-9 The Pythagorean Theorem (continued) The distance from the top of the ladder to the ground is about 9.7 ft. 4-9

  4. = / a2 + b2 = c2Use the Pythagorean Theorem. The longest side, 12 cm, is the hypotenuse. Substitute a = 6, b = 8, and c = 12. 62 + 82 122 36 + 64 144 Simplify. 100 144 Add. COURSE 3 LESSON 4-9 The Pythagorean Theorem Is a triangle with sides 6 cm, 8 cm, and 12 cm a right triangle? The equation is not true, so the triangle is not a right triangle. 4-9

  5. = / no; 82 + 122 162 COURSE 3 LESSON 4-9 The Pythagorean Theorem 1. The bottom of a 12-ft ladder is 4 ft from the side of a house. Find the height of the top of the ladder above the ground to the nearest tenth. 2. Is a triangle whose sides are 8 m, 12 m, and 16 m a right triangle? Explain. 11.3 ft 4-9

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