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how to find the third vertex

Known two vertices A(x1,y1) and B(x2,y2) of a triangle, how to find the third vertex C(x3,y3)? Also known the length of AB as a units and angle B = alpha degrees.

Well i wud like to know the general method(which include only variables) to find the third vertex, So that i can get the result just by applying the formula.

The only unknowns angle A,angle C,length of BC and length of CA.

I tried to figure it out assuming that a cirlce that passes thru these three vertices as shown in the attachment..............

But i cud'nt succeed. Please help me.