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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