Trigonometry Calculate Distance and Angle of object in camera frame

I have an application where I am trying to build a handheld scanner that can draw a 2d profile of a 3d surface (using structured light scanning). The handheld device consists of a line laser and a camera. I know the distance between the camera and the laser, the cameras focal length, the line lasers angle of projection, and the angle between the laser and the camera. What I do not know is the distance and rotation of the surface being scanned because this will vary (handheld device will no be stationary). My question is, is what I am trying to do mathematically possible with my set of knowns and unknowns.

Structured light scanning relies on the deformation that happens to the laser line as it contours to the shape of the object (for more info see here: https://en.wikipedia.org/wiki/Structured-light_3D_scanner).

Please see my attached drawing for clarification. Any help or a point in the right direction will be greatly appreciated!

3dScanner