I am currently working on a school project that requires me to create a device that points a laser at any arbitrary point on a flat surface below it, by rotating it along the $X$ and $Y$ axis.
The pointer is a known distance $A$ above the middle of the plane, so if we were only dealing with one direction we could treat it like a right triangle and find the required angle $a$ via the equation $a=\tan^{-1} \frac XA$.
However, I don't think this would remain true while working with two dimensions at once. Looking more closely at it, I also noticed that we are effectively pointing at a point in a imaginary sphere, so polar coordinates may be related, but its been a long time since i learned about polar coordinates and I don't remember them well enough to know if it is related or not.
On a small second point, the laser is technically redirected by rotating two mirrors, instead of the laser itself, and due it's design the laser is rotated in one direction first before travelling several milimeters and bouncing off a second rotating mirror. Because of this, while the laser effectively originates from a stationary point on the first mirror, it does move along the surface of the second mirror. Does this complicate the problem or is it effectively the same?