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Charlie Plesums, Austin, Texas, USA

This is a simple table that anyone can calculate!

Assume that you are starting with a standard American 8.5 inch by 11 inch sheet of paper. If you wanted a 45 degree angle, you would simply fold the paper diagonally. Or think of it as cutting the long side of the paper to 8.5 inches, and looking at the diagonal. You now have a triangle with two 45 degree angles (and a 90 degree angle).

If you wanted a 40 degree angle (and a 50 degrees and 90 degrees in the rest of the triangle). Cut the long side of the paper at 10 1/8 inches (leaving the short side at 8 1/2 inches) and use the diagonal again. Of course as the angle gets smaller, we need to go out more than 11 inches. Or we need to shorten the 8 1/2 inch side.

The table below shows the possible dimensions of the paper that has a diagonal at the desired angle. Simple trigonometry.

Small AngleLarge AngleSmall SideLarge Side
0908 1/211
1893/1611
2883/811
3879/1611
4863/411
58515/1611
6841 1/811
7831 3/811
8821 9/1611
9811 3/411
10801 15/1611
11792 1/811
12782 5/1611
13772 9/1611
14762 3/411
15752 15/1611
16743 1/811
17733 3/811
18723 9/1611
19713 13/1611
20704 11
21694 1/411
22684 7/1611
23674 11/1611
24664 7/811
25655 1/811
26645 3/8 11
27635 5/8 11
28625 7/8 11
29616 1/8 11
30606 3/8 11
31596 5/8 11
32586 7/8 11
33577 1/8 11
34567 7/1611
35557 11/1611
3654811
37538 5/1611
38528 1/210 7/8
39518 1/210 1/2
40508 1/210 1/8
41498 1/29 3/4
42488 1/29 7/16
42478 1/29 1/8
44468 1/28 13/16
45458 1/28 1/2

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