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: 67

Answer

Refer to the step by step section below.

Work Step by Step

Assume I have $A,a,b$ given (works similarly for other cases.) By the Law of Sines($\frac{{\sin {A}}}{a} = \frac{{\sin {B}}}{b} = \frac{{\sin {C}}}{c}$) I can get one of the other two angles. (Here $\sin {B}=b\frac{{\sin {A}}}{a}\\B=\sin^{-1}{(b\frac{{\sin {A}}}{a})}.$ Then as we know the sum of the $3$ angles is $180^o$ so I count the third degree by subtracting the sum of the know two angles from $180^o$. (Here $C=180^o-(A+B).$ Finally, by the Law of Sines I can get the final side. (Here: $c=b\frac{{\sin {C}}}{\sin {B}}).$
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