Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.1 - Angles and Radian Measure - Exercise Set - Page 533: 96

Answer

The required solution is $\text{698}\ \text{miles}$

Work Step by Step

The radius of the earth $ r $ is $4000\ \text{miles}$. The angle $\theta $ at the center between A and B is $10{}^\circ $. So, convert $\theta $ into radians: $\begin{align} & \theta =10{}^\circ \left( \frac{\pi }{180{}^\circ } \right) \\ & =\frac{\pi }{18} \end{align}$ And the distance $ s $ between A and B is given by $ s=r\theta $ Put $4000\ \text{miles}$ for $ r $ and $\frac{\pi }{18}$ for $\theta $: $\begin{align} & s=\left( 4000\ \text{miles} \right)\left( \frac{\pi }{18} \right) \\ & =\frac{2000\pi }{9}\ \text{miles} \end{align}$ Put $\pi =3.14159$: $\begin{align} & s=\frac{2000\left( 3.14159 \right)}{9}\ \text{miles} \\ & \text{=698}\text{.13}\approx \text{698}\ \text{miles} \end{align}$
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