make a diagram, label the base of the tower T, and let the height of the tower be h
let AT=x, then TB = 1.1-x
in 1st triangle:
tan6 = h/x ---> h = xtan6
in 2nd triangle:
tan 13 = h/(1.1-x) --> h = (1.1-x)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.
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.
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