Draw a segment of length a, label the ends B and C.

At the end of the segment labelled C construct the given angle C and produce the arm at angle C to segment a.

Mark point D a distance b-c along this arm.

On the segment DB as base construct and isosceles triangle having one of the equal sides on CD produced.

Draw a line parallel to the new side of this isosceles triangle through B.

Label the point that this meets CD produced A.

Triangle ABC is the required triangle.

RonL