## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises: 21

b=1.2 miles

#### Work Step by Step

The hypotenuse is 1.3 miles and one of the legs is 0.5 miles. Use the Pythagorean theorem ( $a^{2}$ + $b^{2}$ = $c^{2}$) and plug in for a and c to get $.5^{2}$ + $b^{2}$ = $1.3^{2}$.Now solve: $.5^{2}$ + $b^{2}$ = $1.3^{2}$ -do the exponents- 0.25+ $b^{2}$=1.69 -subtract 0.25 from both sides- $b^{2}$=1.44 -find the square root of 1.44 to solve for b- b=1.2 B is 1.2 miles long.

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