Trigonometry! #111

The angles of depression of two ships from the top of a lighthouse are $45^{\circ}$ and $30^{\circ}$ towards east. If the ships are $100m$ apart, then find the height of the lighthouse.

Express your answer in the form of $a(\sqrt{b}+c)m$ , where $a$ , $b$ and $c$ are coprime integers. Enter the value of $a+b+c$ .

This problem is part of the set Trigonometry .