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 - Page 676: 13


$4 \text{ }m$

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=8 $ and $ a=4\sqrt{3} ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ (4\sqrt{3})^2+b^2=8^2 \\\\ 16(3)+b^2=64 \\\\ 48+b^2=64 \\\\ b^2=64-48 \\\\ b^2=16 \\\\ b=\sqrt{16} \\\\ b=4 .\end{array} Hence, the other leg is $ 4 \text{ }m $ long.
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