Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 6 - Section 6.1 - Angle Measure - 6.1 Exercises - Page 479: 64


a. $r\approx 5.86$ b. $r\approx 3.03$

Work Step by Step

The area $A$ of a sector with central angle of $\theta$ radians is $ A=\displaystyle \frac{1}{2}r^{2}\theta$. Solving for r, multiply both sides with $\displaystyle \frac{2}{\theta}$, $\displaystyle \frac{2A}{\theta}=r^{2}\qquad$ ... and take the square root, $r=\sqrt{\dfrac{2A}{\theta}}$ If the angle is in degrees, convert to radians (multiply by $\pi/180^{o}$) a. $ r=\sqrt{\dfrac{2\cdot 12}{0.7}}\approx$5.85540043769 $r\approx 5.86$ b. $150^{o}=\displaystyle \frac{150\pi}{180}$ rad $ r=\sqrt{\dfrac{2\cdot 12}{\frac{150\pi}{180}}}\approx$3.02775902642 $r\approx 3.03$
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