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Angle C is π - (π/4) - (π/3) = 5π/12. The Law of Sines tells you
... a/sin(A) = c/sin(C)
... a = sin(A)·c/sin(C)
... a = sin(π/4)·10/sin(5π/12) ≈ 7.32
The length of the side opposite angle A is about 7.32.
