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Question by lostlyre

Can anyone tell me the formula for finding a missing set of coordinates of a triangle, while knowing two coordinates and three sides?

An ActionScript Snippet Example by birdy1976

// given
var xA = -2;
var yA = -4;
var xB = +5;
var yB = -1;
var a = Math.sqrt(36+16); // exact value
var b = Math.sqrt(49+1); // exact value
// calculation
var xAB = xB-xA;
var yAB = yB-yA;
var c = Math.sqrt(xAB*xAB+yAB*yAB);
var alpha = Math.acos((b*b+c*c-a*a)/(2*b*c));
var epsilon = Math.atan2(yAB, xAB);
var xCA = -b*Math.cos(alpha+epsilon);
var yCA = -b*Math.sin(alpha+epsilon);
var xC = xA-xCA;
var yC = yA-YCA;
trace("("+xC+"|"+yC+")"); // -> C(xC|yC) = C(-1|3)