Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set: 72

Answer

85 ft

Work Step by Step

Because the ceiling forms a 90-degree angle, we use the Pythagorean Theorem, $a^{2}+b^{2}=c^{2}$. We are given the length of two sides, $a$ and $b$. $a=40$ feet and $b=75$ feet. $40^{2}+75^{2}=c^{2}$ Now we must solve for $c^{2}$. Evaluate the exponents: $1600+5625=7225$ $7225=c^{2}$ Solve for $c^{2}$. $\sqrt 7225 = 85$ $85^{2}=7225$ $40^{2}+75^{2}=85^{2}$ Because $c=85$, the length of the speaker wire is $85$ ft.
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