Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.6 Right Triangle Trigonometry - Exercise Set 10.6 - Page 667: 44

Answer

The angle of the elevation to the nearest degree is\[23{}^\circ \].

Work Step by Step

Angle of elevation is the angle made by the horizontal line and the line of sight to an object. Since the angle of elevation opposite to the height of statue and next to the base of the statue. The angle of elevation can be computed by applying the tangent ratio formula: \[\tan \theta =\frac{a}{b}\] Where a; is the side opposite to the angle and b is the side adjacent to the angle. Here, a; is\[555\text{ ft}\]b is\[1320\text{ ft}\]. The value of\[\tan \theta \]can be computed as shown below: \[\begin{align} & \tan \theta =\frac{555\text{ ft}}{1320\text{ ft}} \\ & \tan \theta =0.4204\text{ ft} \\ & \theta ={{\tan }^{-1}}\left( 0.420 \right) \\ & \theta =22.78\approx 23{}^\circ \end{align}\]
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