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: 39


$x = 85.2$ m

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 our given angle. The sine ratio is given as follows: sin $A = \frac{opposite}{hypotenuse}$ Let's plug in what we know: sin $28^{\circ} = \frac{40}{x}$ Multiply each side by $x$: sin $28^{\circ}(x) = 40$ Divide each side by sin $12^{\circ}$ to solve: $x = 85.2$ m
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