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The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m 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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- 4 metre
- 7 metre
- 9 metre
- 6 metre
Correct Option: D
Let, AB = Height of tower = h metre
BC = 4 metre, BD = 9 metre
∠ACB = 90° – θ; ∠ADB = θ
In ∆ABC,
| tan (90° – θ) = | |
| BC |
| ⇒ cotθ = | ..........(i) | |
| 4 |
In ∆ABD,
| tanθ = | ..........(ii) | |
| 9 |
On multiplying both equations,
| tanθ.cotθ = | × | ||
| 4 | 9 |
| = 1 ⇒ h² = 36 | |
| 36 |
⇒ √36 = 6 metre
