Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 6 - Section 6.1 - Angle Measure - 6.1 Exercises - Page 480: 77

Answer

$\approx$ 1037 miles

Work Step by Step

The difference in latitudes gives the central angle of $\theta=40.5^{o}-25.5^{o}=15^{o}$ To convert into radians, multiply by $\pi/180^{o}$. $\displaystyle \theta=\frac{15^{o}\pi}{180^{o}}=\frac{\pi}{12}$ rad The length $s$ of an arc that subtends a central angle of $\theta$ radians is $ s=r\theta$. $ s=\displaystyle \frac{\pi}{12}\cdot 3960\approx$1036.72557568 $\approx$ 1037 miles
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