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Question:

A man in a boat rowing away from a lighthouse 100m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute. [Use √(3) = 1.732]

Solution:

Consider ΔABC
Where AB is Height of Tower
BC is distance from boat to tower
tan C = AB/BC
√3 = 100/BC
BC = 57.73
Now let D be the point the boat travelled
tan D = AB/BD
1/√3 = 100/BD
BD = 173.2
Distance travelled by boat CD = BD - BC = 173.2 - 57.73 = 115.47m
Speed of boat = 115.47/2 = 57.73m/min