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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 Angle	Large Angle	Small Side	Large Side
0	90	8 1/2	11
1	89	3/16	11
2	88	3/8	11
3	87	9/16	11
4	86	3/4	11
5	85	15/16	11
6	84	1 1/8	11
7	83	1 3/8	11
8	82	1 9/16	11
9	81	1 3/4	11
10	80	1 15/16	11
11	79	2 1/8	11
12	78	2 5/16	11
13	77	2 9/16	11
14	76	2 3/4	11
15	75	2 15/16	11
16	74	3 1/8	11
17	73	3 3/8	11
18	72	3 9/16	11
19	71	3 13/16	11
20	70	4	11
21	69	4 1/4	11
22	68	4 7/16	11
23	67	4 11/16	11
24	66	4 7/8	11
25	65	5 1/8	11
26	64	5 3/8	11
27	63	5 5/8	11
28	62	5 7/8	11
29	61	6 1/8	11
30	60	6 3/8	11
31	59	6 5/8	11
32	58	6 7/8	11
33	57	7 1/8	11
34	56	7 7/16	11
35	55	7 11/16	11
36	54	8	11
37	53	8 5/16	11
38	52	8 1/2	10 7/8
39	51	8 1/2	10 1/2
40	50	8 1/2	10 1/8
41	49	8 1/2	9 3/4
42	48	8 1/2	9 7/16
42	47	8 1/2	9 1/8
44	46	8 1/2	8 13/16
45	45	8 1/2	8 1/2

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