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 - Chapter Review - Page 536: 19


$x = 29.9^{\circ}$

Work Step by Step

You would use the Law of Sines here because you have the measure of two sides and a non-included angle, and you need to find the measure of the angle opposite to one of the sides. Let's set up the formula for the Law of Sines to calculate $m \angle x$, the measure of the angle opposite to the side with a length of $11$ ft.: $\frac{sin 115}{20} = \frac{sin x}{11}$ Multiply each side by $11$: $11(\frac{sin 115}{20})$ = sin $x$ Take $sin^{-1}$ of both sides to solve for $x$: $x = 29.9^{\circ}$
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