Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 113: 57


$A=8064.8$ yd$^{2}\approx8060$ yd$^{2}$

Work Step by Step

Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$. Step 2: First, we have to convert the angle from degrees to radians: $40^{\circ}=40(\frac{\pi}{180})=\frac{2\pi}{9}$ radians Step 3: Substituting the values provided by the question into the formula, $A=\frac{1}{2}(152)^{2}(\frac{2\pi}{9})$ Step 4: $A=\frac{23104\pi}{9}$ Step 5: Therefore, $A=8064.8$ yd$^{2}\approx8060$ yd$^{2}$
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