Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

APPENDIX D - Trigonometry - D Exercises - Page A 35: 77

Answer

$\angle A=62^{\circ}$ $a\approx199.55$ $b\approx241.52$

Work Step by Step

$\angle {A}+ \angle {B}+\angle {C}=180^{\circ}$ $\implies \angle C=180^{\circ}-\angle {A}-\angle {B}$ $=180^{\circ}-50^{\circ}-68^{\circ}=62^{\circ}$ From the law of sines, we have $\frac{\sin C}{c}=\frac{\sin A}{a}$ $\implies a\sin C=c\sin A$ Or $a=c\cdot \frac{\sin A}{\sin C}=230\times\frac{\sin 50^{\circ}}{\sin 62^{\circ}}$ $a\approx 199.55$ Similarly, $\frac{\sin C}{c}=\frac{\sin B}{b}$ $\implies b=c\cdot \frac{\sin B}{\sin C}$ $=230\times\frac{\sin 68^{\circ}}{\sin62^{\circ}}\approx241.52$
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