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There are two vertical posts, one on each side of a road, just opposite to each other. One post is108 metre high. From the top of this post, the angle of depression of the top and foot of the other post are 30° and 60° respectively. The height of the other post (in metre) is
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- 36
- 72
- 108
- 110
Correct Option: B
[ Note : Interior alternate angles
are equal ]
AB = 108 m
CD = x metre
From ∆ ABC,
| tan 60° = | BC |
| ⇒ √3 = | BC |
| ⇒ BC = | = 36√3 m | √3 |
From ∆ AED,
| tan 30° = | ED |
| ⇒ | = | √3 | 36√3 |
⇒ 108 - x = 36
⇒ 108 - x = 36 = 72 m
