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: 40

Answer

$\frac{1}{2}$ m

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 $\theta=180^{\circ}$ and $s=\frac{\pi}{2}$ m. We can convert $\theta$ to radians by multiplying $\theta$ by $\frac{\pi}{180}$. $\theta=180^{\circ}=180(\frac{\pi}{180})=\frac{180\pi}{180}=\pi$ Therefore, $r=\frac{\frac{\pi}{2}}{\pi}=\frac{\pi}{2}\times\frac{1}{\pi}=\frac{\pi}{2\pi}=\frac{\pi\div\pi}{2\pi\div\pi}=\frac{1}{2}$ m.
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