update: new diagram and updated description

I have a contact listener set up to try and determine the side that a collision happened at relative to the a bodies rotation. One way to solve this is to find the value of the yellow angle between the red and blue vectors drawn above. The angle can be found by taking the arc cosine of the dot product of the two vectors (Evan pointed this out). One of my points of confusion is the difference in domain of the atan2 function html canvas coordinates and the Box2d rotation information. I know I have to account for this somehow... SS below

questions:

• Does Box2D provide these angles more directly in the collision information?
• Am I even on the right track? If so, any hints?

I have the following javascript so far:

Ship.prototype.onCollide = function (other_ent,cx,cy) {

  var pos = this.body.GetPosition();

  //collision position relative to body
  var d_cx = pos.x - cx;
  var d_cy = pos.y - cy;

  //length of initial vector
  var len = Math.sqrt(Math.pow(pos.x -cx,2) + Math.pow(pos.y-cy,2));

  //body angle - can over rotate hence mod 2*Pi
  var ang = this.body.GetAngle() % (Math.PI * 2);

  //vector representing body's angle - same magnitude as the first
  var b_vx = len * Math.cos(ang);
  var b_vy = len * Math.sin(ang);

  //dot product of the two vectors
  var dot_prod = d_cx * b_vx + d_cy * b_vy;

  //new calculation of difference in angle - NOT WORKING!
  var d_ang = Math.acos(dot_prod);

  var side; 
  if (Math.abs(d_ang) < Math.PI/2 )
    side = "front";
  else
    side = "back"; 

  console.log("length",len);
  console.log("pos:",pos.x,pos.y);
  console.log("offs:",d_cx,d_cy);
  console.log("body vec",b_vx,b_vy);      
  console.log("body angle:",ang);
  console.log("dot product",dot_prod);
  console.log("result:",d_ang);      
  console.log("side",side);
  console.log("------------------------");

}