construct triangle ABC,given b-c,a,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.