math
posted by Denisha on .
I'm not sure how to work this problem out. Find it very confusing and my answer keeps changing. Please help.
From an observation tower that overlooks a runway, the angles of depression of point A, on one side of the runway, and point B, on the opposite side of the runway are 6 degrees and 13 degrees, respectively. The points and the tower are in the same vertical plane and the distance from A to B is 1.1 km. Determine the height of the tower.

make a diagram, label the base of the tower T, and let the height of the tower be h
let AT=x, then TB = 1.1x
in 1st triangle:
tan6 = h/x > h = xtan6
in 2nd triangle:
tan 13 = h/(1.1x) > h = (1.1x)tan13
then xtan6 = 1.1tan13  xtan13
xtan6 + xtan13 = 1.1tan13
x(tan6  tan13) = 1.1tan13
x = 1.1tan13/(tan6 + tan13)
once you found x, sub that into h = xtan6
to get the height.