Fun with triangles and polynomials

Geometry Level 5

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

x324x2+180x420=0.x^3-24x^2+180x-420=0.

If the value of sinA+sinB+sinC=pq\sin A+\sin B+\sin C=\dfrac{p}{q}, where p,qp, q are coprime positive integers, find p+q10p+q-10.


Inspiration

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