Solution:
Let AB be the lighthouse and ships are at point C and D.
AB = 100 metre
In △ABC,
tan 45° = AB / BC
⇒ 1 = 100 / BC ⇒ BC = 100 metre
In △ABD,
tan 30° = AB / BD
⇒ 1/√3 = 100 / BD
⇒ BD = 100 × √3
= 100 × 1.73 = 173 metre
Distance between two ships = CD
= BC + BD = 100 + 173
= 273 metre