An aircraft at C is spotted by two observers at A and B who

An aircraft (at C) is spotted by two observers (at A and B) who are L = 1650 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 alpha = 50degree,and beta = 50degree, how high is the airplane ? The elevation of the plane is approximately feet.

Solution

Let base length AD = x

tan(alpha) = h/AD

tan50 = h/x

x = h/tan50 =0.84h ----(1)

Let base lenght BD =y

tan50 = h/y

y = h/tan50 =0.84h -----(2)

Given L = x+y = 1650

So, 0.84h +0.84h = 1650

h = 982.14 feet