1. The Pythagorean Theorem
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.
a2 + b2 = c2 Use the Pythagorean Theorem.
= c2 Substitute a = 6, b = 8.
= c2 Simplify.
100 = c2 Add.
100 = c2 Find the positive square root of each side.
10 = c Simplify.
The length of the hypotenuse is 10 ft.
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2. The Pythagorean Theorem
COURSE 3 LESSON 4-9
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 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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3. The Pythagorean Theorem
COURSE 3 LESSON 4-9
(continued)
a2 + b2 = c2
Use the Pythagorean Theorem.
a2 + (2.5)2 = 102
Substitute b = 2.5 and c = 10.
a = 100
Multiply.
a2 = 93.75
Subtract 6.25 from each side.
Use a calculator.
a =
Find the positive square root.
a Round to the nearest tenth.
The distance from the top of the ladder to the ground is about 9.7 ft.
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4. The Pythagorean Theorem
COURSE 3 LESSON 4-9
The Pythagorean Theorem
Is a triangle with sides 6 cm, 8 cm, and 12 cm a right triangle?
a2 + b2 = c2 Use the Pythagorean Theorem.
The longest side, 12 cm, is the hypotenuse. Substitute a = 6, b = 8, and c = 12.
Simplify.
Add. = /
The equation is not true, so the triangle is not a right triangle.
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5. The Pythagorean Theorem
COURSE 3 LESSON 4-9
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
no; = /
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