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?

100(√3 + 1) m

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