## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson

# Chapter 5 - Trigonometric Functions - Chapter Review - Review Exercises - Page 459: 49

#### Answer

$\dfrac{\pi}{3}=1.0472 \approx1.047 \ ft$ and $\dfrac{\pi}{3} \approx1.047 \ ft^2$

#### Work Step by Step

The arc length is given by: $=(r) (\dfrac{\theta}{180}) ( \pi)=(2) \cdot (\dfrac{30}{180}) \cdot \pi=\dfrac{\pi}{3}=1.0472 \approx1.047 \ ft$ The area of a sector is given by: $A=\dfrac{\theta}{360}\cdot \pi \cdot r^2$ ( $\theta$ is in degrees) Now, $A=\dfrac{30}{360}\cdot \pi \cdot 2^2=\dfrac{120 \pi }{360} =\dfrac{\pi}{3} \approx1.047 \ ft^2$

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