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 = 40degree, and beta = 25degree, how high is the airplane? The elevation of the plane is approximately feet.

Solution

let us say the distance between A and D is \'x\' feet

and distance between D and B is \'y\' feet

then x+y =L

x+y =1650 feet

tan(alpha) = h/x

tan(40) = h/x

1/tan40 = x/h ------------>1

tan(beta) = h/y

tan25 = h/y

1/tan25 = y/h -------------------->2

add 1 and 2

1/tan40 + 1/tan25 = x/h +y/h

1.19 + 2.13 = (x+y) /h

3.32= L/h

h = 1650/3.32

h = 496.98795feet

the elevation of plane is approximately 496.99 feet