Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 90 m high, the distance (in m) between the two ships is?
Answer & explanation
Correct answer: option 1
In ΔABC;
tan 45° = 1 : 1
(AB) : (BC)
↓ ↓
90m (90 m)
AB = height of lighthouse = 90 m
In ΔABD;
tan 30° = 1 : \(\sqrt {3}\)
(AB) : (BD)
↓ ↓
90 90 × \(\sqrt {3}\) = 90\(\sqrt {3}\)
distance between ships = DB + BC = 90\(\sqrt {3}\) + 90 = 90(\(\sqrt {3}\) + 1) m