Determine how far the plane is from point A and B

Question

Observers at points A and B, 60 km apart, sight an airplane at angles of elevation of 50° and 72°, respectively. Use this information to determine how far the plane is from each observer if the plane is between them.

Determine how far the plane is from A and B

Answer 1

A and B 50 and 72 degrees, 60 km apart

A to plane

B to plane

(60+x)tan50=xtan72

x(tan50-tan72)=-60

x= 60/(tan72-tan50)= 31.815

plane to ground = 31.815tan72= 97.8 km

A to plane = 97.8csc50 = 127.69 km

B to plane - 97.8csc72 = 102.85 km