Answer
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.
