Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set: 14

Answer

$\sqrt{31}\approx5.568 \text{ }cm$

Work Step by Step

Let the right triangle have $a$ and $b$ as the legs and $c$ as the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ c=6 $ and $ a=\sqrt{5} ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ (\sqrt{5})^2+b^2=6^2 \\\\ 5+b^2=36 \\\\ b^2=36-5 \\\\ b^2=31 \\\\ b=\sqrt{31} .\end{array} Hence, the other leg is $ \sqrt{31}\approx5.568 \text{ }cm $ long.
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