Trigonometry (10th Edition)

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

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 105: 34

Answer

12.66 cm

Work Step by Step

Arc length s (for central angle $\theta$):$ \quad s=r\theta$, where $\theta$ is in radians Converting between Degrees and Radians 1. Multiply a degree measure by $\displaystyle \frac{\pi}{180}$ radian and simplify to convert to radians. 2. Multiply a radian measure by $\displaystyle \frac{180^{\mathrm{o}}}{\pi}$ and simplify to convert to degrees. ------------------- The weight will be raised for the length of the arc of the pulley as it rotates through the given angle. The angle needs to be in radians $\displaystyle \theta=(51.6)\cdot\frac{\pi}{180}=\frac{51.6\pi}{180}$ Solve for r, inserting values for s and $\theta:$ $ s=r\theta$ $11.4=r\displaystyle \cdot\frac{51.6\pi}{180}$ $ r=\displaystyle \frac{11.4\cdot 180}{51.6\pi}\approx$12.6583698924 ... about 12.66 cm.
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