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There are two temples, one on each bank of a river, just opposite to each other. One temple is 54m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. The length of the temple is :
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- 18 m
- 36 m
- 36 √3 m
- 18 √3 m
Correct Option: B
AB = temple = 54 metre
CD = temple = h metre
BC = width of river
= x metre
From ∆ABC,
| tan 60° = | BC |
| ⇒√3 = | ⇒ x = | x | √3 |
⇒ 18√3 metre
From ∆ ADE
| tan 30° = | DE |
| &rArr | = | √3 | 18√3 |
⇒54 – h = 18
⇒ h = 54 – 18 = 36 metre
