The angles of depression of two ships from the tops of a light house are $45^{\circ}$ and $30^{\circ}$ towards east. If the ships are $100\;m$ apart, the height of the light house is _______

Question

$\begin{array}{1 1}(A) \; \frac{50}{\sqrt 3 +1} \;m \\(B)\; \frac{50}{\sqrt 3 -1}\;m \\(C)\;50 (\sqrt 3 -1) \\(D)\;50 (\sqrt 3 +1) \end{array}$