# Trigonometry! #119

Geometry Level 3

A tower is $$50m$$ high. Its shadow is $$x~m$$ shorter when the sun's altitude is $$45^{\circ}$$ than when it is $$30^{\circ}$$. Then find the value of $$x$$.

Express the value of $$x$$ in the form of $$\frac{a}{b}$$ where $$a$$ and $$b$$ are relatively prime, and enter the value of $$a+b$$.

This problem is part of the set Trigonometry.

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