Page 357 - Basic College Mathematics with Early Integers

334 C HAPTE R 4 I DECIMALS

PRACTICE 7 Example 7 Approximate the length of the hypotenuse of the given right
Approximate the length of the triangle. Round the length to the nearest whole unit.
hypotenuse of the given right
10 m
triangle. Round to the nearest
whole unit.

17 m
7 km

9 km
Solution:

2 2
hypotenuse = 21leg2 + 1other leg2
2 2
= 21172 + 1102 The legs are 10 meters and 17 meters.
= 2289 + 100
= 2389
L 20 From Appendix A.6 or a calculator
The hypotenuse is exactly 2389 meters, which is approximately 20 meters.

Work Practice 7

PRACTICE 8 Example 8 Find the length of the leg in the given right triangle. Give the
Find the length of the leg in exact length and a two-decimal-place approximation.
the given right triangle.
Give the exact length and
a two-decimal-place 5 in.
approximation.

7 in.
Solution: Notice that the hypotenuse measures 7 inches and that the length of
11 ft one leg measures 5 inches. Since we are looking for the length of the other leg, we
use the formula
2 2
leg = 21hypotenuse2 - 1other leg2
7 ft
Putting the known values into the formula, we have
2 2
leg = 2172 - 152 The hypotenuse is 7 inches, and the other leg is 5 inches.
= 249 - 25

= 224 Exact answer
L 4.90 From Appendix A.6 or a calculator
The length of the leg is exactly 224 inches, which is approximately 4.90 inches.

Work Practice 8
Copyright 2012 Pearson Education, Inc.

Answers Concept Check The following lists are the lengths of the sides of two trian-
7. 11 km gles.Which set forms a right triangle? Explain.
8. 272 ft L 8.49 ft
a. 8, 15, 17 b. 24, 30, 40
Concept Check Answer
set (a) forms a right triangle