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Trigonometry Word Problems

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A flagpole 5 m high stands on top of a building. From a point P on the street, the angle of elevation of the top of the pole is 32 degrees and the angle of elevation on the bottom of the pole is 30 degrees. How tall is the building?

Solution
Let AB represent the building (with point A on the street) and BC represent the flagpole.
Let x be the building height.
AB = x; AC = x+5
AP is the distance between the building and point P on the street.

Then tan (32 deg.) = (5+x)/AP
tan (30 deg.) = x/AP

From these two equations we get,

(5+x)/0.625 = x/0.577

2.877 + 0.577 x = 0.625 x
So, x = 60.15 m = Height of the building.

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