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 - Study Summary - Practice Exercises - Page 692: 17


$10 \text{ and } 5\sqrt{3}\approx8.660$

Work Step by Step

The side opposite the $30^o$ angle of a right triangle measures half as long as the hypotenuse. Hence, the hypotenuse is $10.$ 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=10 $ and $ a=5 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 5^2+b^2=10^2 \\\\ 25+b^2=100 \\\\ b^2=100-25 \\\\ b^2=75 \\\\ b=\sqrt{75} \\\\ b=\sqrt{25\cdot3} \\\\ b=\sqrt{(5)^2\cdot3} \\\\ b=5\sqrt{3} .\end{array} Hence, the missing measurements are $ 10 \text{ and } 5\sqrt{3}\approx8.660 $ units long.
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