Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 261: 112

Answer

$\theta = \pi - arctan(\frac{75}{100-x}) - arctan(\frac{150}{x})$

Work Step by Step

Let $~A~$ be the angle between the ground and the short building. $tan~A = \frac{75}{100-x}$ $A = arctan(\frac{75}{100-x})$ Let $~B~$ be the angle between the ground and the tall building. $tan~B = \frac{150}{x}$ $B = arctan(\frac{150}{x})$ We can find an expression for $\theta$: $A+\theta+B = \pi$ $\theta = \pi - A - B$ $\theta = \pi - arctan(\frac{75}{100-x}) - arctan(\frac{150}{x})$
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