Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.4 - Arc Length and Area of a Sector - 3.4 Problem Set - Page 155: 38

Answer

$\frac{4}{3}$ cm

Work Step by Step

We know that the length of the arc $s$ cut off by $\theta$ can be calculated as $s=r\theta$. Therefore, we also know that $r=\frac{s}{\theta}$. We are given that $\theta=\frac{3\pi}{4}$ and $s=\pi$ cm. Therefore, $r=\frac{\pi}{\frac{3\pi}{4}}=\pi\times\frac{4}{3\pi}=\frac{4\pi}{3\pi}=\frac{4\pi\div\pi}{3\pi\div\pi}=\frac{4}{3}$ cm.
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