Trigonometry (10th Edition)

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

Chapter 3 - Review Exercises - Page 129: 27

Answer

$\approx 4,468\text{ km}$

Work Step by Step

Find the measure of the central angle between $28^oN$ and $12^oS$. The $12^oS$, since it goes clockwise from the equator, can be represented by $-12^o$, Thus, the measure of the central angle between the two cities is: $=28^o-(-12^o) \\=28^o+12^o \\=40^o$ Convert the angle measure to radians by multiplying it by $\dfrac{\pi}{180^o}$ to obtain: $\require{cancel} =40^o \times \dfrac{\pi}{180^o} \\=\cancel{40^o}^2 \times \dfrac{\pi}{\cancel{180^o}9} \\=\dfrac{2\pi}{9}$ 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: $s=r\theta \\s=6400 \text{ km} \times \dfrac{2\pi}{9} \\s\approx 4,468\text{ km}$
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