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The two banks of a canal are straight and parallel. A, B, C are three persons of whom A stands on one bank and B and C on the opposite banks. B finds the angle ABC is 30°, while C finds that the angle ACB 60°. If B and C are 100 metres apart, the breadth of the canal is
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25 metres √3 - 20 √3 metres
- 25 √3 metres
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20 metres √3
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Correct Option: C
BD = x metre (let)
∴ CD = (100 – x) metre
AD ⊥ BC; AD = y metre
From ∆ ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | x |
⇒ x = √3 y
From ∆ACD ....(i)
| tan 60° = | 100 - x |
| ⇒ √3 = | 100 - x |
⇒ y = 100 √3 - √3 x
⇒ y = 100 √3 - √3 × √3 y
⇒ y = 100 √3 - 3y
7rArr; 4y = 100 √3
⇒ y = 25 √3 metre
