the angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. prove that the height of the tower is 6 m
The given situation can be represented as,
Let height of the tower be h m.
Given, the angles of elevation of the top of tower from the two points are complementary.
∴ ∠ACB = θ and ∠ADB = 90 – θ
∴ Height of the tower = h = 4 tan θ = 4 × = 6 m (Using (1))
Thus, the height of the tower is 6 m.