a man on the top of a cliff 'x' meters high observes that the angle of elevation of the tower is equal to the angle of depression of the foot of the tower. The height of the tower in meters is
Answers
Given : a man on the top of a cliff 'x' meters high observes that the angle of elevation of the tower is equal to the angle of depression of the foot of the tower.
To find : The height of the tower in meters is
Solution :
Let say angle of elevation of the tower = α = angle of depression of the foot of the tower
Let say horizontal Distance between cliff & tower = b
Tan α = x/b
=> b Tanα = x
Let say height of tower be h
then height of tower above cliff will be h - x
Tan α = (h - x) / b
=> b Tan α = h - x
Equating b Tanα
=> x = h - x
=> h = 2x
height of the tower in meters is 2x m
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