Sins ain't bad

Geometry Level 3

ABCABC is a triangle with side lengths 5,5, 42,4\sqrt2, and 7. 7.

Another triangle has side lengths sinA,\sin A, sinB,\sin B, and sinC. \sin C.

If the area of that triangle is pq,\frac{p}{q}, where pp and qq are coprime positive integers, then what is p+q?p+q?

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