Question

the angles of elevation of top of a tower from two points at distance a and b meters from the base and in the same straight line with it are complementary. prove that the height of the tower is √ab

Answer 1

Let small dist (from base P to pt. Q) be a meters and larger dist (from P to S) be b meters.
Height = h meters

Angle of elevation from pt. Q
tan theta = h/ a.

Angle from pt. S
tan(90-theta) = h/ b.
cot theta= h/ b
1/tan theta =h/ b

Using tan theta = h/ a.

1/(h/ a)= h/ b
a/h = h/b
h^2 = (ab)^2
Therefore, h= root ab

Hence proved.

Answer 2

Answer:

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