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The angular elevation of the top of a tower from a distant point on the horizontal ground is observed to be 30° and proceeding 30 metres from the point towards the foot of the tower it is observed to be 45°. Find the height of the tower.
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- 15 metre
- 15√3
- 15 (√3 + 1) metre
- None of these
- 15 metre
Correct Option: C
AB = tower = h metre
BD = x metre
From ∆ABC,
| tan 30° = | |
| BC |
| ⇒ | = | ||
| √3 | x + 30 |
→ √3h = x + 30 ....(i)
From ∆ABD,
| tan45° = | |
| BD |
→ h = x .......(ii)
From equation (i)
→ √3h = x + 30
→ (√3 - 1)h = x + 30
| ⇒ h = | = | × | = | = 15(√3 + 1) metre | ||||
| √3 - 1 | √3 - 1 | √3 + 1 | 2 |
