Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 8 - Applications of Trigonometric Functions - 8.2 The Law of Sines - 8.2 Assess Your Understanding - Page 534: 66


I first solve for the measure of the third angle, then by the law of sines compute the lengths of the other two sides.

Work Step by Step

As we know the sum of the $3$ angles is $180^o$ so find the measure of the third angle by subtracting the known two angles from $180^o$. Then by the Law of Sines $\left(\dfrac{{\sin {A}}}{a} = \dfrac{{\sin {B}}}{b} = \dfrac{{\sin {C}}}{c}\right)$ I can get the other two sides. e.g. if $a$ is known and I have the $3$ angles then $b=a\frac{{\sin {B}}}{\sin {A}}, c=a\frac{{\sin {C}}}{\sin {A}}$.
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