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 - Page 304: 9

Answer

There are no triangles which can be formed with the given parts.

Work Step by Step

We can use the law of sines to find the angle $B$: $\frac{a}{sin~A} = \frac{b}{sin~B}$ $sin~B = \frac{b~sin~A}{a}$ $sin~B = \frac{(61)~sin~(58^{\circ})}{50}$ $sin~B = 1.0346$ Since there is no angle $B$ such that $sin~B \gt 1$, the angle $B$ is not defined. There are no triangles which can be formed with the given parts.
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