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