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A man standing on the bank of river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36 m from the bank, he finds that the angle is 30°. The breadth of the river is
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- 15 metre
- 18 metre
- 16 metre
- 11 metre
Correct Option: B
AB = tree = h metre
BC = width of river = x metre
CD = 36 metre
From ∆ ABC,
| tan 60° = | BC |
| ⇒ √3 = | x |
⇒ h = √3 x metre .... (i)
From ∆ ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | x + 36 |
⇒ √3 h = x + 36
⇒ √3 × √3 x = x + 36
⇒ 3x – x = 36
⇒ 2x = 36
⇒ x = 18 metre
