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: 71

Answer

75 feet

Work Step by Step

Because the tower 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 $b$. $a=45$ feet and $b=60$ feet. $45^{2}+60^{2}=c^{2}$ Now we must solve for $c^{2}$. Evaluate the exponents: $2025+3600=5625$ $5625=c^{2}$ Solve for $c^{2}$. $\sqrt 5625 =75$ $75^{2}=5625$ $45^{2}+60^{2}=75^{2}$ Because $c=75$, the length of the cable is $75$ ft.
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