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Two observers A and B stand 1 km apart on a level road. A plane directly above the road between them is seen at elevations of 60° from A and 30° from B. How high is the plane?

Competition practiceTrigonometry
  • A250√3 m
  • B500 m
  • C500√3 m
  • D250 m

Step-by-Step Solution

h cot 60° + h cot 30° = 1000, i.e. h(1/√3 + √3) = 4h/√3 = 1000, so h = 250√3 m ≈ 433 m.
Answer: A) 250√3 m

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