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 = 1100 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 = 45 degree, and beta = 45 degree, how high is the airplane? The elevation of the plane is approximately square feet. (Do not round until the final answer. Then round to two decimal places as needed.)

Solution

Let AD = x

So, applying rt angled triangle propert in triangle ACD :

tan45 = h/x

applying rt angled triangle propert in triangle BCD :

tan45 = h/(1100 -x)

Now divide both the equations we get:

1 = 1100-x/x

x= 1100 -x

x= 550 feet

Height of plane h = x = 550 feet