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 - Page 106: 56


$365.3$ m$^{2}$

Work Step by Step

First converting $125^{\circ}$ to radians: $125^{\circ}=125(\frac{\pi}{180})=\frac{25\pi}{36}$ radians The formula for the area of a sector of a circle having radius $r$ and central angle $\theta$ is $A=\frac{1}{2}r^{2}\theta$. Substituting the values of $r$ and $\theta$ into the formula: $A=\frac{1}{2}(18.3)^{2}(\frac{25\pi}{36})$ Solving through a calculator: $A=\frac{1}{2}(18.3)^{2}(\frac{25\pi}{36})\approx365.3$ m$^{2}$
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