Calculating the coordinates of the third point of a triangle

Question

OK, I know this sounds like it should be asked on math.stackoverflow.com, but this is embarrassingly simple maths that I\'ve forgotten from high-school, rather than advanced pos

Answer 1

EDIT: I had a serious brainfart previously, but this should work. Use the law of cosines

/* use the law of cosines to get the angle of CAB */
c² = a² + b² - 2ab cos(Cangle)
cos(Cangle) = (a²+b²-c²) / 2ab
Cangle = acos((a²+b²-c²) / 2ab)

AB = B.xy - A.xy;
normalize(AB);
len = length(AC)
C.x = len*AB.x* cos(Cangle) * len*AB.y*sin(Cangle);
C.y = len*AB.x*-sin(Cangle) * len*AB.y*cos(Cangle);