Computing the dimensions of an isosceles trapezoid only knowing one base, its angles, and the area

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Is it possible to compute b and c's of an isosceles trapezoid given values for area (A), one base (a), and the angle off of that base (α)? I thought I could break this down into determining the area of the 2 right triangles made up from from c, height, and (b-a)/2, but I got nowhere fast with that approach.