# Trigonometry! #125

Geometry Level 3

In $$\Delta ABC$$, the sides $$a$$, $$b$$ and $$c$$ are the roots of the equation $x^{3}-11x^{2}+38x-40=0$ Then find the value of $\displaystyle\sum_{\text{cyclic}}\frac{\cos A}{a}$ Express your answer in the form of $$\frac{p}{q}$$ where $$p$$ and $$q$$ are coprime positive integers. Enter the value of $$p+q$$.

This problem is part of the set Trigonometry.

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