I am having trouble understanding special angles. I had forgotten…

I am having trouble understanding special angles. I had forgotten about them, and I am totally lost in reviewing them for this year’s maths. I need to understand it quickly so u can move on. These are the really simple basics, but i am just missing something.
Here is a note I took about it. I don’t understand what is going on. for the 30,60, and 90 triangles, I don’t know where the 1, 2 and underoot 3 came from? Are these some standard values or are they random? I don’t understand where the value for 4, for the r, came from. I know that r is hypotenuse, but I don’t understand where that value had come from. I also don’t understand why they have mirrored the triangle to solve for the underoot 3 value.
I don’t really know at all what is occurring for the degenerate angle.
Below are some problems, that you dont need to answer for my question, but the problems are regarding the above note, so it would be helpful.
I also don’t know what is going on here.
I am missing some simple rules that I am not remembering and would like help in understanding them.

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