Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 11 - Section 11.3 - The Tangent Ratio and Other Ratios - Exercises - Page 519: 2


$\tan\alpha=\frac{15}{8}$ $\tan\beta=\frac{8}{15}$

Work Step by Step

Let $x$ be the side of the triangle with an unknown length. Using Pythagorean Theorem to find $x$. $x=\sqrt{17^{2}-15^{2}}$ $x=8$ $\tan\alpha=\frac{opposite}{hypotenuse}=\frac{15}{x}=\frac{15}{8}$ $\tan\beta=\frac{opposite}{hypotenuse}=\frac{x}{15}=\frac{8}{15}$
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