An aircraft at Z is spotted by two observers at X and Y who

An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1350 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure. If A = 30 degree, and B = 30 degree, how high is the airplane? The elevation of the plane is approximately feet.

Solution

Drop the altitude from Z to D, with height h
given A = 30

and B = 30
AD = h cot30
DB = h cot30

AD+dB = 1350

h cot30 + h cot30 = 1350

2 h cot30 = 1350

h cot30 = 675

h = 675 / cot30

h = 389.711431703 ft