Question
A boat is being rowed away from a cliff 183 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?(approx.)Solution
According to the figure above: Cot 45° = (AD/AB) = 1= (AD/183) = 183 m Also, Cot 60° = (AC/AB) = (1/ √3 ) = (AC/150) = AC = (183/√3 ) m Therefore AC = (183 x √3 )/(√3 x √3) = 61√3 = 61 x 1.73 = 105.5 m Therefore CD = AD - AC = (183 - 105.5) = 77.5 m Speed of Boat = 77.5/180 m/s ((77.5/180) x (18/5) ) km/hr (1395/900) = 1.5km/hr
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