## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 10 - Geometry - Chapter Summary, Review, and Test - Review Exercises: 22

#### Answer

$a\approx 10.2$ cm

#### Work Step by Step

RECALL: The Pythagorean Theorem states that in a right triangle, $c^2=a^2+b^2$ where: $a$ and $b$ are the lengths of the legs (non-hypotenuse sides) $c$ is the length of the hypotenuse Use the Pythagorean Theorem with c = 15 and b = 11 to obtain: $15^2 = a^2 + 11^2 \\225=a^2+121 \\225-121=a^2 \\104=a^2$ Take the square root of both sides to obtain: $\pm \sqrt{104} = a$ Use a scientific calculator to obtain: $\pm 10.19803903 = a \\\pm 10.2 \approx a$ Since $a$ represents a length, it cannot be negative. Thus, $a\approx 10.2$ cm

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