Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises: 73

Answer

$\color{blue}{s\approx 55.3 \text{ in}}$

Work Step by Step

RECALL: The length of the arc $(s)$ intercepted by the central angle $\theta$ in a circle of radius $r$ is given by the formula: $s = r\theta$, where $\theta$ is in radian measure. Convert the angle to radians by multiplying $\dfrac{\pi}{180^o}$ to the angle measure to obtain: $210^o=210^0 \cdot \dfrac{\pi}{180^o}=\dfrac{7\pi}{6}$ Use the formula above to obtain: $s=r\theta \\s=15.1 \cdot \frac{7\pi}{6} \\s=55.34439058 \\\color{blue}{s\approx 55.3 \text{ in}}$
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