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 - Skill Practice - Page 856: 15



Work Step by Step

We need to use the Pythagorean Theorem in order to solve $y$ such that $r^2=x^2+y^2 \implies y=\sqrt {r^2-x^2}$ $y=\sqrt{(9)^2-(4)^2}=\sqrt{65}$ Since, $\tan \theta=\dfrac{Opposite}{Adjacent}=\dfrac{y}{x}$ Thus, $\tan \theta=\dfrac{\sqrt{65}}{4}$
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