Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises - Page 576: 109


$\color{blue}{A \approx 8,060 \space yd^2}$

Work Step by Step

RECALL: The area of a sector $(A)$ intercepted by a central angle $\theta$ on a circle whose radius is $r$ is given by the formula: $A = \frac{1}{2}r^2\theta$, where $\theta$ is in radian measure. Convert the angle measure to radians by multiplying $\dfrac{\pi}{180^o}$ to the given angle to obtain: $40.0^o \\=40\cdot\dfrac{\pi}{180^o} \\=\dfrac{2\pi}{9}$ Substitute the given values of the the central angle and radius to obtain: $A=\frac{1}{2}r^2\theta \\A=\frac{1}{2}(152^2)(\frac{2\pi}{9}) \\A=8,064.817408 \\\color{blue}{A \approx 8,060 \space yd^2}$
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