Question

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 40 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)

Answer 1

Let:

x = Distance between the fire and the Pine Knob tower

y = Distance between the fire and the Colt station fire tower

We can find x and y using the law of sines:

$\begin{gathered} \frac{40}{sin(30)}=\frac{x}{sin(135)} \\ so: \\ x=\frac{40\cdot sin(135)}{sin(30)} \\ x=40\sqrt{2} \\ x\approx56.57km \end{gathered}$$\begin{gathered} \frac{40}{sin(30)}=\frac{y}{sin(15)} \\ y=\frac{40\cdot sin(15)}{sin(30)} \\ y=20\sqrt{6}-20\sqrt{2} \\ y\approx20.71km \end{gathered}$