The Pythagorean Theorem

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Presentation transcript:

The Pythagorean Theorem COURSE 2 LESSON 8-6 Find the length of the hypotenuse. c2 = a2 + b2 Pythagorean Theorem c2 = 212 + 202 Substitute. c2 = 441 + 400 Simplify. c2 = 841 Take the square root of each side. c2 = 841 c = 29 The length of the hypotenuse is 29 in. 8-6

The Pythagorean Theorem COURSE 2 LESSON 8-6 Find the missing leg of the triangle. a2 + b2 = c2 Pythagorean Theorem a2 + 152 = 252 Substitute. a2 + 225 = 625 Simplify. a2 + 225 – 225 = 625 – 225 Subtract 225 from both sides. a2 = 400 Simplify. a = 20 Take the square root of each side. a2 = 400 The length of the leg is 20 ft. 8-6

The Pythagorean Theorem COURSE 2 LESSON 8-6 A ladder, placed 4 ft from a wall, touches the wall 11.3 ft above the ground. What is the approximate length of the ladder? Draw a diagram to illustrate the problem. c2 = a2 + b2 Use the Pythagorean Theorem. c2 = 42 + 11.32 Substitute. c2 = 143.69 c2 = 16 + 127.69 Square 4 and 11.3. Add. Use a calculator. Take the square root of each side. c = 11.98708 c2 = 143.69 The length of the ladder is about 12 ft. 8-6

The Pythagorean Theorem COURSE 2 LESSON 8-6 Find the length of the missing side of each right triangle to the nearest tenth. 1. legs of 4 cm and 6 cm 2. leg of 9 m, hypotenuse of 15 m 3. leg of 36 ft, hypotenuse of 39 ft 4. legs of 28 cm and 45 cm 7.2 cm 12 m 15 ft 53 cm 8-6