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: 21


$x \approx 17.5$

Work Step by Step

In this exercise, we are given the measure of a non-included side and two angles. We can use the law of sines to find the measure of another line in the triangle. The law of sines states the following: $\frac{sin A}{a}$ = $\frac{sin X}{x}$ Let's plug in what we know into the formula: $\frac{sin 40}{12}$ = $\frac{sin 110}{x}$ Multiply each side by $x$: $\frac{sin 40}{12}(x)$ = sin $110$ Divide both sides by $\frac{sin 40}{12}$ to solve for $x$: $x \approx 17.5$
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