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: 48

Answer

$240^{\circ}$

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: Substituting the values in the question, $96\pi=\frac{1}{2}(12^{2})\theta$ Step 3: Multiplying both sides by 2, $96\pi\times2=\frac{1}{2}\times(12^{2})\times\theta\times2$ Step 4: $192\pi=144\theta$ Step 5: Multiplying both sides by $\frac{1}{144}$, $192\pi\times\frac{1}{144}=144\theta\times\frac{1}{144}$ Step 6: $\theta=\frac{4\pi}{3}$ Step 7: Converting radians to degrees, $\frac{4\pi}{3}=\frac{4\pi}{3}(\frac{180^{\circ}}{\pi})=240^{\circ}$ Step 8: Therefore, the required angle is $240^{\circ}$.
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.