As observed from the top of a lighthouse, 60 m high above sea the angle of depression of a ship changes from 45° to 60°. The distance travelled by the ship during the period of observation is?
Answer & explanation
Correct answer: option 2
AB represents lighthouse = 60 m
distance travelled by ship = CD
In ΔABD,
tan 45° = 1 : 1
(AB) (BD)
↓ ↓
60 60 m
In ΔABC,
tan 45° = \(\sqrt {3}\) : 1
(AB) (BC)
↓ ↓
60 \(\frac{60}{\sqrt {3}}\) = \(\frac{60 \sqrt {3}}{3}\) = 20 \(\sqrt {3}\)
Therefore, CD = BD - BC = 60 - 20 \(\sqrt {3}\) = 20(3 - \(\sqrt {3}\)) m