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A helicopter, at an altitude of 1500 metre, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 30° respectively. Distance between the two ships, in metre is
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1000 √3 - 1000 √3
- 500 √3
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500 √3
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Correct Option: A
AD = Height of helicopter = 1500 metre
C and D ⇒ positions of ships
∠ADB = 30°; ∠ACB = 60°
Let, BC = x metre and BD = y metre
In ∆ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | y |
⇒ y = 1500 √3 metre ...(i)
In ∆ABC,
| tan 60° = | BC |
| ⇒√3 = | x |
| ⇒x = | √3 |
= 500 √3 metre ...(ii)
∴ Distance between ships
= (y – x) metre
= (1500 √3 500 √3 - ) metre
= 1000 √3 metre
