Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 8 - Right Triangles and Trigonometry - 8-4 Angles of Elevation and Depression - Practice and Problem-Solving Exercises - Page 521: 40

Answer

$x = 38.2$ ft.

Work Step by Step

Since we have the measure of one angle and the measure of the hypotenuse, we can use the sine ratio to find $x$, which is the side opposite to the given angle. The sine ratio is given as follows: sin $A = \frac{opposite}{hypotenuse}$ Let's plug in what we know: sin $24^{\circ} = \frac{x}{94}$ Multiply each side by $94$: sin $24^{\circ}(94) = x$ Multiply to solve: $x = 38.2$ ft.
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