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: 27


$B =60^{\circ}$, $a = 5.77$ and $c=11.54$

Work Step by Step

We have: $B=180^{\circ}-30^{\circ}-90^{\circ}=60^{\circ}$ Use Law of Sines to find side $a$: $\dfrac{\sin B}{b}=\dfrac{\sin A}{a}$ This implies that $a=\dfrac{10 \sin 30^{\circ}}{\sin 60^{\circ}} \implies a \approx 5.77^{\circ}$ Use Law of Sines to find side $c$: $\dfrac{\sin A}{a}=\dfrac{\sin C}{c}$ This implies that $c=\dfrac{5.77 \sin 90^{\circ}}{\sin 30^{\circ}} \implies a \approx 5.77^{\circ}$ Our answers are: $B =60^{\circ}$, $a = 5.77$ and $c=11.54$
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