Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 6 - 6.2 - Right Triangle Trigonometry - 6.2 Exercises - Page 443: 66


The height of the mountain is 1.295 miles.

Work Step by Step

To solve for the elevation, we need to set up a proportion: The first equation will be for the small triangle: tan($9^{o}$) = $\frac{y}{x}$ where y is the elevation of the mountain and x is the distance from the mountain to the first point. The second equation will be for the larger triangle: tan($3.5^{o}$) = $\frac{y}{13 + x}$ Solving the system of equations: x = 8.17 miles y = 1.295 miles Therefore, the height of the mountain is 1.295 miles.
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