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From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on the same side of the pillar, then the height of the pillar is
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- 5 m
- 10 m
- 7 m
- 12 m
Correct Option: D
AB = Pole = h metre
BC = 9 metre BD = 16 metre
∠ADB = θ ;
∴ ∠ACB = 90° – θ
From ∆ABC,
| tan (90° – θ) = | BC |
| ⇒ cotθ = | ......(i) | 9 |
from ∆ABD
| ⇒ tanθ = | ......(ii) | 16 |
By multiplying (i) & (ii)
| tanθ . cotθ = | × | |||
| 9 | 16 |
| ⇒ | = 1 | 144 |
⇒ h2 = 144
⇒ h = √144 = 12 metre
