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From the top of a building 60 metre high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower in metre is :
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- 40
- 45
- 50
- 55
Correct Option: A
AB = Height of building = 60 metre
CD = Height of tower = h metre
∠FAD = ∠ADE = 30°
∠FAC = ∠ACB = 60°
From ∆ABC,
| tan60° = | |
| BC |
| ⇒ √3 = | |
| BC |
| ⇒ BC = | = 20√3 metre = DE | |
| √3 |
From ∆ADE,
| tan 30° = | |
| ED |
| ⇒ | = | ||
| √3 | 20√3 |
⇒ h = 60 – 20 = 40 metre
