Question

Two radar stations are 50 miles apart. Both are tracking the same plane. At this moment, the angle between station 1 and the plane is 73 degrees and the angle between station 2 and the plane is 46 degrees. How far is the plane from station 2?

Answer 1

By "the angle" I assume you mean the angle between the line from the station to the plane and the line joining the stations. In that case,

Label the diagram as follows.
A = station 1
B = station 2
P = plane
Q = point on AB closes to the plane PQ┴AB)
y = PQ
a = AQ
x = PB (the desired distance)

y/a = tan 73°
y/(50-a) = tan 46°
eliminating the a, we have

y/tan73° = 50 - y/tan46°
y = 39.326

Now, the distance x=PB is found using

y/x = sin 46°
x = 39.326/sin46° = 54.67