Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Review Exercises - Page 349: 1


63.7 m

Work Step by Step

The law of sines in the case of this question is: $\frac{b}{\sin B}=\frac{c}{\sin C}$ We substitute the values of $B,C$ and $c$ in the formula to find $b$: $\frac{b}{\sin B}=\frac{c}{\sin C}$ $\frac{b}{\sin 39.5}=\frac{96.3}{\sin 74.2}$ $b\times \sin 74.2=96.3\times \sin 39.5$ $b=\frac{96.3\times\sin 39.5}{\sin 74.2}$ We use a calculator to find the values of $\sin 39.5$ and $\sin 74.2$: $b=\frac{96.3\times\sin 39.5}{\sin 74.2}$ $b=\frac{96.3\times 0.63608}{0.96222}$ $b=63.660\approx63.7$ Therefore, $b=63.7$ m.
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