Question 55

Two points P and Q are at the distance of x and y (where y > x) respectively from the base of a building and on a straight line. If the angles of elevation of the top of the building from points P and Q are complementary, then what is the height of the building?

Solution

BP =x and BQ=y
AB =h
Now Tan p =h/x    (1)
Tan Q=h/y    (2)
Now Q=90-P
So Tan Q = Cot P = 1/Tan P
So we get h/x =y/h
we get h^2 =xy
h = $$\sqrt{\ xy}$$


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