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 100 m high, the distance (in m) between the two ships is?
Answer & explanation
Correct answer: option 4
In ΔABC;
tan 45° = 1 : 1
(AB) : (BC)
↓ ↓
100 m (100 m)
AB = height of lighthouse = 100 m
In ΔABD;
tan 30° = 1 : \(\sqrt {3}\)
(AB) : (BD)
↓ ↓
100 100 × \(\sqrt {3}\) = 100\(\sqrt {3}\)
distance between ships = DB + BC = 100\(\sqrt {3}\) + 100 = 100(\(\sqrt {3}\) + 1) m