Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Review Exercises - Page 129: 23

Answer

$49.06^{\circ}$

Work Step by Step

The formula to be used here is $s=r\theta$ where $s$ is the arc length, $r$ is the radius and $\theta$ is the angle in radians. Next, we rearrange the formula to $\theta=\frac{s}{r}$ because $s$ and $r$ are known and $\theta$ is the unknown. Substituting the values of $r=8.973$ cm and $s=7.683$ cm into the formula and solving using a calculator: $\theta=\frac{s}{r}=\frac{7.683}{8.973}\approx0.8562$ radian Converting radians to degrees: $0.8562$ radian=$0.8562(\frac{180}{\pi})=49.06^{\circ}$
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