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From the top of a 50 m high lighthouse, the angles of depression of two ships on the same side, in line with its foot, are 30° and 60°. How far apart are the ships?

Competition practiceTrigonometry
  • A100/√3 m
  • B50√3 m
  • C100√3 m
  • D50/√3 m

Step-by-Step Solution

Distances: 50 cot 30° = 50√3 and 50 cot 60° = 50/√3. Difference = 50√3 − 50/√3 = 100/√3 m ≈ 57.7 m.
Answer: A) 100/√3 m

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