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: 60

Answer

The radius of the circle is 15.6 m.

Work Step by Step

Let $\theta$ be the angle in radians. Let $A$ be the area of the sector. Then the ratio of the angle to $2\pi$ is equal to the ratio of the sector area to the area of the whole circle. $\frac{\theta}{2\pi} = \frac{A}{\pi ~r^2}$ $r^2 = \frac{2A}{\theta}$ $r = \sqrt{\frac{2A}{\theta}}$ $r = \sqrt{\frac{(2)(64~m^2)}{(\pi/6)}}$ $r = 15.6~m$ The radius of the circle is 15.6 m.
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