# Chapter 7 - Review Exercises - Page 349: 4

$b=70.9$ 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.

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