Find the length of the hypotenuse of a right triangle whose

legs are 6 ft and 8 ft.

The Pythagorean TheoremThe Pythagorean TheoremCOURSE 3 LESSON 4-9COURSE 3 LESSON 4-9

The length of the hypotenuse is 10 ft.

a2 + b2 = c2 Use the Pythagorean Theorem.

62 + 82 = c2 Substitute a = 6, b = 8.

36 + 64 = c2 Simplify.

100 = c2 Add.

100 = c2 Find the positive square root of each side.

10 = c Simplify.

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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?

The Pythagorean TheoremThe Pythagorean TheoremCOURSE 3 LESSON 4-9COURSE 3 LESSON 4-9

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.

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(continued)

The Pythagorean TheoremThe Pythagorean TheoremCOURSE 3 LESSON 4-9COURSE 3 LESSON 4-9

The distance from the top of the ladder to the ground is about 9.7 ft.

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.

93.75 9.6824584 Use a calculator.

a = 93.75 Find the positive square root.

a 9.7 Round to the nearest tenth.

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Is a triangle with sides 6 cm, 8 cm, and 12 cm a right triangle?

The Pythagorean TheoremThe Pythagorean TheoremCOURSE 3 LESSON 4-9COURSE 3 LESSON 4-9

The equation is not true, so the triangle is not a right triangle.

a2 + b2 = c2 Use the Pythagorean Theorem.

62 + 82 122 The longest side, 12 cm, is the hypotenuse. Substitute a = 6, b = 8, and c = 12.

36 + 64 144 Simplify.

100 144 Add.=/

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The Pythagorean TheoremThe Pythagorean Theorem1. 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

COURSE 3 LESSON 4-9COURSE 3 LESSON 4-9

no; 82 + 122 162=/

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