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 - 8-6 Law of Cosines - Practice and Problem-Solving Exercises - Page 531: 19


$x = 59.0^{\circ}$

Work Step by Step

You would use the Law of Sines here because you have the measure of two sides and one 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 $8$: $\frac{sin 40}{6} = \frac{sin x}{8}$ Multiply each side by $8$: $8(\frac{sin 40}{6})$ = sin $x$ Take $sin^{-1}$ to solve for $x$: $x = 59.0^{\circ}$
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