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From the peak of a hill which is 300 m high, the angle of depression of two sides of a bridge lying on a ground are 45° and 30° (both ends of the bridge are on the same side of the hill). Then the length of the bridge is
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- 300( √3 – 1) m
- 300( √3 + 1) m
- 300 √3 m
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300 m √3
Correct Option: A
AB = hill = 300 metre
CD = bridge = x metre
In ∆ABC,
| tan 45° = | BC |
| ⇒ 1 = | BC |
⇒ BC = 300 metre
In ∆ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | 300 + x |
⇒ 300 + x = 300 √3
⇒ x = 300 √3 – 300
= 300 ( √3 – 1) metre
