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A helicopter flies horizontally at a steady height of 600 m along a straight level road. At one instant the angle of depression of a parked car on the road ahead is 30°; twenty seconds later it is 60°. The distance flown by the helicopter in those twenty seconds is:

Competition practiceTrigonometry
  • A600√3 m
  • B1200√3 m
  • C200√3 m
  • D400√3 m

Step-by-Step Solution

The car is parked, so only the helicopter's horizontal position changes. At the first sighting it is 600·cot30° = 600√3 ≈ 1039.2 m short of the car, at the second 600·cot60° = 600/√3 = 200√3 ≈ 346.4 m. The distance flown is the difference, 600√3 − 200√3 = 400√3 ≈ 692.8 m (a speed of about 34.6 m/s). The two horizontal distances themselves, 600√3 ≈ 1039.2 m and 200√3 ≈ 346.4 m, are the near-miss answers — reporting either one answers 'how far from the car', not 'how far flown' — and 1200√3 doubles the first distance, which no part of the geometry calls for.
Answer: D) 400√3 m

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