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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