Fink of an equilateral triangle, OK? Internal angles are all 60º, all sides are length 1.
SO now fink of all those one degree lines drawn in, from one apex. The distance from the apex to the line opposite side is , in
plumbing terms, also 1 (actually .866 or something I can't be bothered to work out).
SO every degree is represented, roughly, by a length of line equal to 1/60th.
SO a degree is about 1 in 60

,
3º is 1 in 20,
= a fingers thickness per foot.
Similarly, old bog pan outlets are 14º. 1 in 4 is much easier to work with!
If you've got your kid's cally handy, the ratio is
1 in 1/(tan[number of degrees])