Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - Cumulative Test for Chapters 6-8 - Page 621: 25


$B \approx26.39^{\circ}$, $c \approx 15^{\circ}$ and $C=123.61^{\circ}$

Work Step by Step

Use law of sines to find angle $B$: $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$ This implies that $\sin B=\dfrac{8 \sin 30^{\circ}}{9} \implies B \approx 26.39^{\circ}$ and $C=180^{\circ}-30^{\circ}-26.39^{\circ}=123.61^{\circ}$ Use law of sines to find $c$: $\dfrac{a}{\sin A}=\dfrac{c}{\sin C}$ This implies that $c=\dfrac{9 \sin 123.61^{\circ}}{\sin 30^{\circ}} \implies c \approx 15^{\circ}$ Our answers are: $B \approx26.39^{\circ}$, $c \approx 15^{\circ}$ and $C=123.61^{\circ}$
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