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Question
The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 metres.
The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 metres.
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Solution
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.
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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