## Precalculus (6th Edition) Blitzer

Here, the fire is denoted at point C at the distance b from station A. We will apply the sine rule to calculate the distance but at first we will calculate the angle. By using the figure, calculate the angle $\angle A,\angle B$ and $\angle C$, \begin{align} & \angle A\,=\,90{}^\circ -50{}^\circ \\ & =40{}^\circ \end{align} \begin{align} & \angle B=\,90{}^\circ -40{}^\circ \\ & =50{}^\circ \end{align} And, \begin{align} & \angle C=\,180-50{}^\circ -40{}^\circ \\ & =90{}^\circ \end{align} The distance of side c is given, so we will apply the sine law, $\frac{b}{\sin B}=\frac{c}{\sin C}$ Here, $c=1.6\,\,\text{miles},\,\angle B=50{}^\circ \,$ and $\angle C=90{}^\circ$. Now by putting the value in the equation, we get: \begin{align} & \frac{b}{\sin 50{}^\circ }=\frac{1.6}{\sin 90{}^\circ } \\ & \frac{b}{0.766}=\frac{1.6}{1} \\ & b\approx 1.0\,\,\text{mile} \end{align}