Fire lookout towers are used to locate fires so they can be put out as soon as possible. These towers often work in networks and if two towers can see a fire at the same time, they can determine the location of the fire vey accurately.

Question

Fire lookout towers are used to locate fires so they can be put out as soon as possible. These towers often work in networks and if two towers can see a fire at the same time, they can determine the location of the fire vey accurately. 
A.) Two forest rangers in towers see a fire. The angle at Tower A between tower B and the fire is measured to be 41.5 degrees. The angle at tower B between tower A and the fire is measured to be 87.3 degrees. If the towers are known to be 34.32 km apart, how far is the fire from each tower? (I know I need to use Sine, but I don't know how to complete the calculations)

Reiny · Answer

You are right, you have to use the sine law
Since you know 2 angles, we can find the angle at F to be 51.2°

So AF/sin87.3 = 34.32/sin51.2
AF = 34.32sin87.3/sin51.2
calculator time .....
AF = 43.988...

repeat similar steps to find BF