Precalculus (10th Edition)

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

Chapter 6 - Trigonometric Functions - Chapter Review - Review Exercises - Page 435: 49

Answer

The Arc Length:$1.047\text{ft}$. The Area of sector:$1.047\text{ft}^2.$

Work Step by Step

The Arc Length can be counted by: $s=r\cdot \frac{\theta}{180}\cdot \pi.$ Here $s=2\cdot \frac{30}{180}\cdot \pi=\frac{\pi}{3}=1.0472\approx1.047\text{ft}$. The Area of sector can be counted by: $A=\frac{\theta}{360}\cdot \pi \cdot r^2$,where $\theta$ is in degrees, hence $A=\frac{30}{360}\cdot \pi \cdot 2^2=\frac{\pi}{3}\approx1.047\text{ft}^2.$
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