Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 7 - Applications of Trigonometric Functions - Section 7.1 Right Triangle Trigonometry ; Applications - 7.1 Assess Your Understanding - Page 541: 58



Work Step by Step

The trigonometric functions can be expressed as: $\sin \theta=\dfrac{Opposite}{Hypotenuse} \\ \cos \theta=\dfrac{Adjacent}{Hypotenuse} \\ \tan \theta=\dfrac{Opposite}{Adjacent}$ We are given the opposite side and adjacent side. Our aim is to compute the the angle. So we use Tangent. Let $a$ be the height of the ladder that touches the building and consider it as the opposite side. Since, $\tan \theta=\dfrac{Opposite}{Adjacent}$ Therefore, $\tan \theta=\dfrac{3}{12} \implies \theta =\arctan (\dfrac{3}{12})$ or, $\theta \approx 14.03^{\circ}$
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