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From the top of a 150 m high cliff, the angle of depression of a boat sailing straight towards the cliff changes from 30° to 45° in 2 minutes. The speed of the boat is:

Competition practiceTrigonometry
  • A150(√3 − 1) m/min
  • B75(√3 + 1) m/min
  • C75(√3 − 1) m/min
  • D75√3 m/min

Step-by-Step Solution

The boat's distances from the foot of the cliff are 150/tan30° = 150√3 m and 150/tan45° = 150 m. It covers 150√3 − 150 = 150(√3 − 1) m in 2 minutes, so the speed is 75(√3 − 1) m/min ≈ 54.9 m/min.
Answer: C) 75(√3 − 1) m/min

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