Question
A boat is being rowed away from a cliff 240 m high. From
the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 3 minutes. What is the speed of the boat?Solution
According to the figure above: tan 45° = 240/(a + b) ⇒ 1 = 240/(a + b) ⇒ a + b = 240 Also, tan 60° = 240/a ⇒ √ 3 = 240/a ⇒ a = 240/ √ 3 ⇒ a = 80√ 3 = 138.5 ∴ b = 240 - 138.5 = 101.5 ⇒ The boat covers a distance of 101.5 m in 3 minutes. ∴ Speed of the boat = (101.5 x 60)/(3 x 1000) km/h = 2.03 km/h
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