# Trigonometry! #111

Geometry Level 1

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.

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