Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 5 - Trigonometric Functions - Section 5.1 Angles and Their Measures - 5.1 Assess Your Understanding - Page 387: 96


$\frac{8}{9}\text{ radians} \approx 0.89\text{ radians}$

Work Step by Step

We have: radius $r=15\text{ yards}$ area = $100 \text{ square yards}$ The formula for the area of a sector is given by the formula $A=\frac{1}{2}r^{2}\theta$ where $\theta$ is the central angle in radians and $r$ is the radius. Use this formula to obtain: $\frac{1}{2}\times(15)^{2}\times\theta=100$ $\frac{225}{2}\times\theta=100$ $\theta=100 \times \frac{2}{225}$ $\theta=\frac{8}{9}\text{ radians}\approx 0.89\text{ radians}$
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