# math

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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.

• math -

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.

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