Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.6 - Radical Equations and Problem Solving - Exercise Set: 58

Answer

$\sqrt{12.58} \text{ } in \text{ OR } \approx 3.5 \text{ } in$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Pythagorean Theorem to solve for the value of the missing side measurement. $\bf{\text{Solution Details:}}$ Based on the given figure, the missing side is the hypotenuse, $c,$ of the right triangle. Using the Pythagorean Theorem which is given by $c^2=a^2+b^2,$ with $a= 2.7 $ and $b= 2.3 ,$ then \begin{array}{l}\require{cancel} c^2=2.7^2+2.3^2 \\\\ c^2=7.29+5.29 \\\\ c^2=12.58 .\end{array} Taking the principal square root of both sides (since there are no negative side measurement) results to \begin{array}{l}\require{cancel} c=\sqrt{12.58} .\end{array} Hence, the missing side is $ \sqrt{12.58} \text{ } in \text{ OR } \approx 3.5 \text{ } in .$
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