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Question
The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove tht the height of the tower is √ab metre.
The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove tht the height of the tower is √ab metre.
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Solution
Answer :
AB is a tower. D and Care two points on the same side of a tower, BD = a and BC = b.
∠ADB and ∠ACB are the complementary angles.
If ∠ADB = x, then ∠ACB = 90 – x
In ∆ADB,
………… (1)
In ∆ABC,
…………....(2)
Multiplying (1) and (2),
(AB)2 = ab
AB = √ab
Height of tower = AB = √ab
AB is a tower. D and Care two points on the same side of a tower, BD = a and BC = b.
∠ADB and ∠ACB are the complementary angles.
If ∠ADB = x, then ∠ACB = 90 – x
In ∆ADB,
………… (1)
In ∆ABC,
…………....(2)
Multiplying (1) and (2),
(AB)2 = ab
AB = √ab
Height of tower = AB = √ab
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