I'm looking to find the width and height of a rectangle without rotation within a rotated bounding rectangle. I have rotation in degrees and the width and height of the bounding rectangle. Basically I'm looking to find the largest ( largest area ) un-rotated rectangle that will fit inside a rotated rectangle of any given size.
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If you don't have the coordinates of the rotated corners, just rotate each point.
Once you have that, find the smallest and largest $x,y$ coordinates of the 4 points.
The smallest and largest $x,y$ pairs correspond to the bottom-left and top-right corners of your rectangle.