before I go further I want you to know that I'm developing a collision detection system in a programming language (Javascript).
I'm not used to math terms (it was like 10 years ago when I was in school), but I think this should be simple:
I need the formula to find this angle.
In the picture you can see I need the angle of the first vertex, but I also need the formula to find the other angles to the bottom right vertex, the bottom left vertex and so on.
Although the rectangle size is variable, I have access to its width and height, and also the X,Y coordinate of its center point.
Thank you beforehand!
To find the "bearings" (angles) to the rectangle's vertices, all that is needed are the height (the vertical, Y direction: let's call it $h$) and the width (the horizontal, X direction: let's call it $w$). The coordinates of the center are not needed.
The upper-right vertex has bearing $\tan^{-1}\frac wh$ where $\tan^{-1}$ is the arctangent function, sometimes called $\operatorname{atan}$ or $\arctan$. I believe in javascript you would write
$$\operatorname{Math.atan}(w/h)$$
and the answer would be an angle in radians.
The lower-right vertex has bearing
$$\operatorname{Math.PI}-\operatorname{Math.atan}(w/h)$$
The lower-left vertex has bearing
$$\operatorname{Math.PI}+\operatorname{Math.atan}(w/h)$$
and the upper-left vertex has bearing
$$2*\operatorname{Math.PI}-\operatorname{Math.atan}(w/h)$$
Do you need further explanation of these formulas?