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

In ∆ABC,

In ∆ABD,

∴ Height of the tower = *h* = 4 tan θ = 4 × = 6 m (Using (1))

Thus, the height of the tower is 6 m.

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