Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises: 77

Answer

$\color{blue}{s\approx 5900\text{ km}}$

Work Step by Step

Since they are in opposite directions from the equator, the central angle between the two cities is: $=41^o+12^o=53^o$ Convert the angle to radians by multiplying $\dfrac{\pi}{180^o}$ to the angle measure to obtain: $=53 \cdot \dfrac{\pi}{180^o}=\dfrac{53\pi}{180}$ RECALL: The length of the arc $(s)$ intercepted by the central angle $\theta$ in a circle of radius $r$ is given by the formula: $s = r\theta$, where $\theta$ is in radian measure. Use the formula above to obtain: $s=r\theta \\s=6400 \cdot \frac{53pi}{180} \\s=5920.156823 \\\color{blue}{s\approx 5900\text{ km}}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.