Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Review Exercises - Page 129: 28

Answer

$\approx 11,952\text{ km}$

Work Step by Step

Find the measure of the central angle between $72^oE$ and $35^oW$. $35^oW$ can be represented by $-35^o$ as it is measured going to the left., Thus, the measure of the central angle between the two cities is: $=72^o-(-35^o) \\=72^o+35^o \\=107^o$ Convert the angle measure to radians by multiplying it by $\dfrac{\pi}{180^o}$ to obtain: $\require{cancel} =107^o \times \dfrac{\pi}{180^o} \\=\dfrac{107\pi}{180}$ The distance between the two cities, which $s$, is is given by the formula $s=r\theta$ where r = radius and $\theta$= central angle measure in radians. Therefore, the distance between the two cities is: $s=r\theta \\s=6400 \text{ km} \times \dfrac{107\pi}{180} \\s\approx 11,952\text{ km}$
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