# Fun with triangles and polynomials

Geometry Level 5

It is given that $$a, b, c$$ are sides of a triangle $$\Delta ABC$$ and the roots of the equation below.

$x^3-24x^2+180x-420=0.$

If the value of $$\sin A+\sin B+\sin C=\dfrac{p}{q}$$, where $$p, q$$ are coprime positive integers, find $$p+q-10$$.

Inspiration

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