CAT 2018 Trigonometry — Previous Year Question

A boat, stationed at the North of a lighthouse, is making an angle of $30^\circ$ with the top of the lighthouse. Simultaneously, another boat, stationed at the East of the same lighthouse, is making an angle of $45^\circ$ with the top of the lighthouse. What will be the shortest distance between these two boats? The height of the lighthouse is $300$ feet. Assume both the boats are of negligible dimensions.