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: 26


$B \approx 67.22^{\circ}$, $C \approx 82.78^{\circ}$ and $a \approx 5.04$

Work Step by Step

Use Law of Cosines to find $a$: $a=\sqrt {b^2+c^2-2bc \cos A}=\sqrt{(8)^2+(10)^2-(2)(8) \cos 30^{\circ}} \approx 5.04$ Use Law of Cosines to find $B$: $\dfrac{a}{\sin A}=\dfrac{C}{\sin A}$ This implies that $\sin C=\dfrac{10 \sin 30^{\circ}}{5.04} \implies C \approx 82.78^{\circ}$ and $B=180^{\circ}-30^{\circ}-82.78^{\circ}=67.22^{\circ}$ Our answers are: $B \approx 67.22^{\circ}$, $C \approx 82.78^{\circ}$ and $a \approx 5.04$.
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