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The distance between two pillars of length 16 metres and 9 metres is x metres. If two angles of elevation of their respective top from the bottom of the other are complementary to each other, then the value of x (in metres) is
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- 15
- 16
- 12
- 9
Correct Option: C
From ∆ABC,
| tan (90° – θ) = | x |
| ⇒ cotθ = | ........(i) | x |
From ∆BCD,
| tanθ = | ........(ii) | x |
| ∴ tanθ . cotθ = | × | |||
| x | x |
⇒ x2 = 16 × 9 [∵ tanθ cotθ =1]
⇒ x = 4 × 3 = 12 metre
