geometry
posted by Sebrenia .
An engineer determines that the angle of elevation from his position to the top of a tower is 55 degrees. The angle of elevation from 75 ft further away is 40 degrees. Determine the height of the tower to the nearest whole number.

Let X be the horizontal distance from which the 55 degree elevation angle was measured.
H/X = tan 55
H/(X + 75) = tan 40
Solve those two equations for H and X.
(X+75)/X = tan 55/ tan 40 = 1.702
1 + 75/X = 1.702
75/X = 0.702
X = 106.8 m
H = 106.8 tan 55 = 153 ft (rounded to nearest integer foot) 
An observer on the ground is x meters from the base of the launch pad of a rocket, which is at the same level as the observer. A few seconds after the rocket takes off vertically, the observer sees its tip at an angle of q° from the horizontal. How far above the ground is the tip of the rocket at that instant? Assume that the ground is level

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