Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Problem Solving - Page 858: 35b


$7263.1$ miles

Work Step by Step

Consider $r$ to be the radius of the tropic of cancer. Let the radius of the Earth be $R$. Then, $\dfrac{r}{R}=\cos \theta \implies R \cos \theta=r$ Since, the circumference of the tropic of cancer is $2 \pi r$. Then, $2 \pi r=2 \pi R \cos \theta \implies 2 \pi (3960) (\cos 23.5)=22817.75$ mile Here, the diameter of the tropic of cancer is equal to $2r$. and $2 r= 2R \cos \theta \implies 2 (3960) (\cos 23.5^{\circ})=7263.1$ miles
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