Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.1 Angles and Their Measure - 6.1 Assess Your Understanding - Page 362: 81


$3.464\text{ feet}$

Work Step by Step

Here, $r$ denotes the radius of the sector of the circle. The Area $A$ of a sector can be computed using the formula $A=\frac{\theta}{2}\cdot r^2$ where $\theta$ is the central angle measure in radians. Hence, here we have $2=\dfrac{\frac{1}{3}}{2}\cdot r^2\\ 2=\frac{1}{6}\cdot r^2\\ 6(2)=\frac{1}{6}r^2(6)\\ 12=r^2\\ r^2=12$ Take the square root of both sides: $\sqrt{r^2}=\pm\sqrt{12}\\ r=\pm\sqrt{12}\\ r=\pm3.4641 r\approx3.464\text{ feet}$ Since $r$ is a radius, it can't be negative. Thus, $r\approx 3.464\text{ feet}$.
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