Page 156 - Math Course 2 (Book 1)

The Pythagorean Theorem

Solve a Right Triangle
Let’s Begin

Example

Find the Length of the Hypotenuse
Find the length of the leg of the right triangle to the
nearest tenth.
Example

8 m 11 m
Find the length of the hypotenuse
of the right triangle.
c ft b m
21 ft
2
2
c = a + b 2 Pythagorean Theorem
112 = 82 + b 2 Replace c with 11 and a
20 ft with 8.
2
2
c = a + b 2 Pythagorean Theorem
121 = 64 + b 2 Evaluate 112 and 82
2
2
c = 21 + 20 2 Replace a with 21 and b
2
with 20. 121 – 64 = 64 + b – 64 Subtract 64 from each side.
2
2
c = 441 + 400 Evaluate 21 and 20 2 57 = b 2 Simplify.
2
2
c = 84 Add 441 and 400. 57 = b Take the square root of
each side.
2
c = 841 Take the square root of
each side. 2nd [ ] 57 ENTER 7.549834435
c = 29

The length of the hypotenuse is Then length of the leg is about
Answer Answer
29 feet. 7.5 meters.

Your Turn!

Find the Length of the Hypotenuse Solve a Right Triangle
Find the length of the hypotenuse Find the length of the leg of the
of the right triangle in meters. right triangle to the nearest tenth.

A. 25 3 m c m A. 7 in. a in 15 in
B. 12.5 B. 12.7 in.
C. 5 4 m C. 13.5 in. 8 in
D. 2.6 D. 17 in.

Answer Answer

148