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: 46

Answer

$75\pi$

Work Step by Step

Step 1: The formula to be used here is $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of the sector of the circle of radius $r$ and central angle $\theta$. Step 2: $A= \frac{1}{2}\times r\times r\times\theta=\frac{1}{2}\times r\times (r\times\theta)=\frac{1}{2}rs$ Step 3: $A=\frac{1}{2}rs=\frac{1}{2}\times10\times15\pi=75\pi$ Step 4: Therefore, the area is $75\pi$.
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