Answer
$b=70.9$ m
Work Step by Step
The law of sines in the case of this question is:
$\frac{a}{\sin A}=\frac{b}{\sin B}$
We substitute the values of $A,a$ and $B$ in the formula to find $b$:
$\frac{a}{\sin A}=\frac{b}{\sin B}$
$\frac{165}{\sin 100.2}=\frac{b}{\sin 25}$
$b\times \sin 100.2=165\times \sin 25$
$b=\frac{165\times\sin 25}{\sin 100.2}$
We use a calculator to find the values of $\sin 25$ and $\sin 100.2$:
$b=\frac{165\times\sin 25}{\sin 100.2}$
$b=\frac{165\times 0.42262}{0.98420}$
$b=70.852\approx70.9$
Therefore, $b=70.9$ m.
