Question
As observed from the top of n lighthouse, 100 m high above sea level, the angle of depression of a ship sailing directly towards it, changes from 30° to 60°. Determine the distance travelled by the ship during the period of observation.
Solution
Height of lighthouse = 100 m
Let distance travelled by the ship, when the angle of depression changes from 60° to 30° (DC) =y m and distance BC = x m Then, in right ∆ABC,
In right 
ABD, tan 
From (i) and (ii), we get
Hence, distance travelled by the ship = 115.473 m.
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