Question
A boat is being rowed away from a cliff 270 m high. From
the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 2 minutes. What is the speed of the boat?Solution
According to the figure above: tan 45° = 270/(a + b) ⇒ 1 = 270/(a + b) ⇒ a + b = 270 Also, tan 60° = 270/a ⇒ √ 3 = 270/a ⇒ a = 270/ √ 3 ⇒ a = 90√ 3 = 155.8 ∴ b = 270 - 155.8 = 114.2 ⇒ The boat covers a distance of 114.2 m in 2 minutes. ∴ Speed of the boat = (114.2 x 60)/(2 x 1000) km/h = 3.4 km/h
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