Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.2 The Ambiguous Case of the Law of Sines - 7.2 Exercises: 20

Answer

The angles are $A=45.40^{\circ}, B=113.72^{\circ}$, and $C=20.88^{\circ}$

Work Step by Step

We can use the law of sines to find the angle $A$: $\frac{b}{sin~B} = \frac{a}{sin~A}$ $sin~A = \frac{a~sin~B}{b}$ $sin~A = \frac{(189.6~yd)~sin~(113.72^{\circ})}{243.8~yd}$ $sin~A = 0.712$ $A = arcsin(0.712)$ $A = 45.40^{\circ}$ We can find angle $C$: $A+B+C = 180^{\circ}$ $C = 180^{\circ}-A-B$ $C = 180^{\circ}-45.40^{\circ}-113.72^{\circ}$ $C = 20.88^{\circ}$ The angles are $A=45.40^{\circ}, B=113.72^{\circ}$, and $C=20.88^{\circ}$
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