Trigonometry (10th Edition)

Published by Pearson

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 105: 33b

Answer

The pulley must be rotated through an angle of $37^{\circ}04'$

Work Step by Step

If the weight rises a height of 6 inches, then a point on the outside of the pulley moves through an arc length $S$ of 6 inches. We can find the angle $\theta$ in radians: $S = \theta ~r$ $\theta = \frac{S}{r}$ $\theta = \frac{6~in}{9.27~in}$ $\theta = 0.647~radians$ We can convert the angle $\theta$ to degrees: $\theta = (0.647~rad)(\frac{180^{\circ}}{\pi~rad})$ $\theta = 37.07^{\circ}$ $\theta = 37^{\circ}+(0.07)(60)'$ $\theta = 37^{\circ}04'$ The pulley must be rotated through an angle of $37^{\circ}04'$

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