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The angle of elevation of the top of a tower from the point P and Q at distance of ‘a’ and ‘b’ respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is
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- √ab
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a b - ab
- a2b2
Correct Option: A
AB = Tower = h units
Let, ∠AQB = θ ∴ ∠APB = 90° – θ
PB = a; BQ = b
From ∆ AQB,
| tanθ = | BQ |
| ⇒ tanθ = | .....(i) | b |
From ∆ APB
| ⇒ tan(90° - θ) = | PB |
| ⇒ cot θ = | ......(ii) | a |
By multiplying (i) & (ii)
| tan θ .cot θ = | × | |||
| b | a |
⇒ h2 = ab
⇒ h = √ab
