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: 58

Answer

$19085.2$ km$^{2}$

Work Step by Step

First converting $270^{\circ}$ to radians: $270^{\circ}=270(\frac{\pi}{180})=\frac{3\pi}{2}$ 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: $A=\frac{1}{2}(90.0)^{2}(\frac{3\pi}{2})$ Solving through a calculator: $A=\frac{1}{2}(90.0)^{2}(\frac{3\pi}{2})\approx19085.2$ km$^{2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.