-
From two points on the ground and 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 distances of the two points from the foot of the pillar are 12 metres and 27 metres and the two points lie on the same side of the pillar, then the height (in metres) of the pillar is
-
- 12
- 18
- 15
- 16
Correct Option: B
Let, ∠ACB = θ
∴ ∠ADB = 90° – θ
BC = 12 metre,
BD = 27 metre
AB = Pillar = h metre
From ∆ABC,
| tan θ = | = | ......(i) | ||
| BC | 12 |
From ∆ABD
| tan(90° – θ) = | BD |
| ⇒ cotθ = | ......(ii) | 27 |
| ∴ tanθ. cotθ = | × | |||
| 12 | 27 |
⇒ h2 = 12 × 27
⇒ h2 = √12 × 27
= √2 × 2 × 3 × 3 × 3 × 3
= 2 × 3 × 3 = 18 metre
