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 668: 48

Answer

The angle that the string makes with the ground is\[27.5{}^\circ \].

Work Step by Step

Angle of elevation is the angle made by the horizontal line and the line of sight’s object. Since the angle of elevation opposite to the height of ramp and next to the hypotenuse of the ramp, use the Sine ratio formula as follows: \[\sin \theta =\frac{a}{c}\] Where a; is the side opposite to the angle and c is the hypotenuse. Here, a; is\[30\text{ ft}\]c is\[65\text{ ft}\]. Compute \[\sin \theta \]can be computed as: \[\begin{align} & \sin \theta =\frac{30\text{ ft}}{65\text{ ft}} \\ & \sin \theta =0.461ft \\ & \theta ={{\sin }^{-1}}\left( 0.461 \right) \\ & =27.5{}^\circ \end{align}\]
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