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A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 40 m from the bank, he finds the angle to be 30°. The breadth of the river is :
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- 40 m
- 60 m
- 20 m
- 30 m
Correct Option: C
Let us draw the figure from the given question.
Let, OA denote the breadth of the river.
Given :- AB = 40 m
In triangle OAP , we have
| OP | = | tan60° | = | √3 |
| OA |
| ∴ | OP | = | √3 OA. |
| Also, In triangle OBP , we have | OP | = | tan 30° | = | 1 |
| OA + 40 | √3 |
| ∴ | OA + 40 = √3 OP = | √3 ( √3 OA ) | = 3 OA. |
| ⇒ | 2OA = 40 | ⇒ | OA = 20 m. |
Hence , the breadth of the river = 20 m .
