# math

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The altitude of the cloud base is particularly important at airports. (The cloud base is where the lowest layer of clouds begins to form.) A bright spotlight is directed vertically upward. It creates a bright spot on the cloud base. From a horizontal distance of 1,150 feet away form the spotlight, the angle of elevation, θ, is measured to be 55°. Find the height of the cloud base (to the nearest foot).

• math -

We form a rt. triangle:
X = 1150Ft. = Hor. side.
Y = Ver. side = Ht of cloud base.
Z = Hyp. = Line of sight.
A = 55 Deg. = Angle bet. hyp. and gnd.

tanA = Y/X
Y = X*tanA = 1150*tann55 = 1642 Ft.

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