KazzLabs

Pythagorean theorem in practice

Definitions of variables in the right triangle

Definition of Unity Distance variable D1

3. Calculation of the right triangle taking into account measurement errors and clearances.

Enter minimum and maximum values of a and b in range from 1 to 9999 and desired accuracy in range from 0,00001 to 0,9 and click "Submit" button.

Maximum 100000 calculations (on the server side) will be performed and only the first 5000 results will be displayed.
Click on column label to change sorting. Rows marked with color are Pythagorean triples.

a	b ↑	c	Δ c	α	90°	max Δ90°	D1(max Δ90°)
4	3	5	0	53.1301°	90.0000°	0.2873°	200
3	4	5	0	36.8699°	90.0000°	0.2873°	200
12	5	13	0	67.3801°	90.0000°	0.1434°	400
8	6	10	0	53.1301°	90.0000°	0.1434°	400
24	7	25	0	73.7398°	90.0000°	0.0956°	600
6	8	10	0	36.8699°	90.0000°	0.1434°	400
15	8	17	0	61.9275°	90.0000°	0.0956°	600
12	9	15	0	53.1301°	90.0000°	0.0956°	600
40	9	41	0	77.3196°	90.0000°	0.0717°	800
24	10	26	0	67.3801°	90.0000°	0.0717°	800
49	10	50	0.0100	78.5215°	89.9415°	0.1221°	470
50	10	51	0.0098	78.6350°	90.0573°	0.1210°	474
60	11	61	0	79.6111°	90.0000°	0.0573°	1 000
5	12	13	0	22.6199°	90.0000°	0.1434°	400
9	12	15	0	36.8699°	90.0000°	0.0956°	600
16	12	20	0	53.1301°	90.0000°	0.0717°	800
35	12	37	0	71.0754°	90.0000°	0.0573°	1 000
48	14	50	0	73.7398°	90.0000°	0.0478°	1 200
8	15	17	0	28.0725°	90.0000°	0.0956°	600
20	15	25	0	53.1301°	90.0000°	0.0573°	1 000
36	15	39	0	67.3801°	90.0000°	0.0478°	1 200
55	15	57	0.0088	74.7772°	89.9653°	0.0788°	728
12	16	20	0	36.8699°	90.0000°	0.0717°	800
30	16	34	0	61.9275°	90.0000°	0.0478°	1 200
63	16	65	0	75.7500°	90.0000°	0.0409°	1 400
71	17	73	0.0068	76.5572°	89.9763°	0.0619°	926
24	18	30	0	53.1301°	90.0000°	0.0478°	1 200
80	18	82	0	77.3196°	90.0000°	0.0358°	1 600
89	19	91	0.0055	77.9654°	89.9831°	0.0506°	1 132
15	20	25	0	36.8699°	90.0000°	0.0573°	1 000
21	20	29	0	46.3972°	90.0000°	0.0478°	1 200
48	20	52	0	67.3801°	90.0000°	0.0358°	1 600
65	20	68	0.0074	72.9174°	89.9780°	0.0557°	1 028
99	20	101	0	78.5788°	90.0000°	0.0318°	1 800
20	21	29	0	43.6028°	90.0000°	0.0478°	1 200
28	21	35	0	53.1301°	90.0000°	0.0409°	1 400
53	21	57	0.0088	68.4075°	89.9743°	0.0594°	964
72	21	75	0	73.7398°	90.0000°	0.0318°	1 800
46	22	51	0.0098	64.4170°	90.0283°	0.0620°	924
79	22	82	0.0061	74.4538°	89.9835°	0.0466°	1 229
64	23	68	0.0074	70.2501°	89.9805°	0.0496°	1 155
7	24	25	0	16.2602°	90.0000°	0.0956°	600
10	24	26	0	22.6199°	90.0000°	0.0717°	800
18	24	30	0	36.8699°	90.0000°	0.0478°	1 200
32	24	40	0	53.1301°	90.0000°	0.0358°	1 600
45	24	51	0	61.9275°	90.0000°	0.0318°	1 800
55	24	60	0.0083	66.4435°	89.9783°	0.0519°	1 105
70	24	74	0	71.0754°	90.0000°	0.0287°	2 000
49	25	55	0.0091	62.9877°	89.9766°	0.0535°	1 071
60	25	65	0	67.3801°	90.0000°	0.0287°	2 000
76	25	80	0.0062	71.8051°	89.9849°	0.0424°	1 353
65	26	70	0.0071	68.2132°	89.9830°	0.0442°	1 296
36	27	45	0	53.1301°	90.0000°	0.0318°	1 800
89	27	93	0.0054	73.1347°	89.9881°	0.0368°	1 556
21	28	35	0	36.8699°	90.0000°	0.0409°	1 400
45	28	53	0	58.1092°	90.0000°	0.0287°	2 000
76	28	81	0.0062	69.7633°	90.0135°	0.0384°	1 493
96	28	100	0	73.7398°	90.0000°	0.0239°	2 400
67	29	73	0.0068	66.6077°	89.9853°	0.0397°	1 445
16	30	34	0	28.0725°	90.0000°	0.0478°	1 200
40	30	50	0	53.1301°	90.0000°	0.0287°	2 000
72	30	78	0	67.3801°	90.0000°	0.0239°	2 400
43	31	53	0.0094	54.2252°	89.9785°	0.0488°	1 175
56	31	64	0.0078	61.0450°	89.9835°	0.0414°	1 384
77	31	83	0.0060	68.0807°	89.9880°	0.0349°	1 641
24	32	40	0	36.8699°	90.0000°	0.0358°	1 600
41	32	52	0.0096	52.0420°	89.9782°	0.0491°	1 167
60	32	68	0	61.9275°	90.0000°	0.0239°	2 400
100	32	105	0.0048	72.2472°	90.0090°	0.0302°	1 899
44	33	55	0	53.1301°	90.0000°	0.0260°	2 200
56	33	65	0	59.4898°	90.0000°	0.0239°	2 400
64	33	72	0.0069	62.7340°	89.9864°	0.0365°	1 571
38	34	51	0.0098	48.1675°	90.0222°	0.0495°	1 159
47	34	58	0.0086	54.1296°	89.9821°	0.0428°	1 338
79	34	86	0.0058	66.7229°	89.9893°	0.0319°	1 798
12	35	37	0	18.9246°	90.0000°	0.0573°	1 000
45	35	57	0.0088	52.1363°	89.9818°	0.0431°	1 330
84	35	91	0	67.3801°	90.0000°	0.0205°	2 800
99	35	105	0.0048	70.5370°	89.9917°	0.0280°	2 045
15	36	39	0	22.6199°	90.0000°	0.0478°	1 200
27	36	45	0	36.8699°	90.0000°	0.0318°	1 800
48	36	60	0	53.1301°	90.0000°	0.0239°	2 400
77	36	85	0	64.9424°	90.0000°	0.0205°	2 800
89	36	96	0.0052	67.9846°	89.9911°	0.0287°	1 997
51	37	63	0.0079	54.0494°	89.9848°	0.0381°	1 504
34	38	51	0.0098	41.8103°	90.0222°	0.0495°	1 159
49	38	62	0.0081	52.2157°	89.9846°	0.0383°	1 496
52	39	65	0	53.1301°	90.0000°	0.0220°	2 600
71	39	81	0.0062	61.2281°	89.9897°	0.0301°	1 904
80	39	89	0	64.0108°	90.0000°	0.0191°	3 000
91	39	99	0.0051	66.8082°	89.9919°	0.0266°	2 158
9	40	41	0	12.6804°	90.0000°	0.0717°	800
30	40	50	0	36.8699°	90.0000°	0.0287°	2 000
42	40	58	0	46.3972°	90.0000°	0.0239°	2 400
55	40	68	0.0074	53.9811°	89.9870°	0.0342°	1 674
75	40	85	0	61.9275°	90.0000°	0.0191°	3 000
96	40	104	0	67.3801°	90.0000°	0.0179°	3 200
32	41	52	0.0096	37.9799°	89.9782°	0.0491°	1 167
53	41	67	0.0075	52.2833°	89.9868°	0.0344°	1 666
64	41	76	0.0066	57.3631°	89.9891°	0.0307°	1 868
79	41	89	0.0056	62.5782°	89.9912°	0.0273°	2 097
40	42	58	0	43.6028°	90.0000°	0.0239°	2 400
56	42	70	0	53.1301°	90.0000°	0.0205°	2 800
31	43	53	0.0094	35.7963°	89.9785°	0.0488°	1 175
59	43	73	0.0068	53.9223°	89.9887°	0.0310°	1 846
71	43	83	0.0060	58.8064°	89.9906°	0.0279°	2 057
33	44	55	0	36.8699°	90.0000°	0.0260°	2 200
57	44	72	0.0069	52.3415°	89.9886°	0.0312°	1 838
68	44	81	0.0062	57.0880°	90.0096°	0.0281°	2 042
24	45	51	0	28.0725°	90.0000°	0.0318°	1 800
28	45	53	0	31.8908°	90.0000°	0.0287°	2 000
35	45	57	0.0088	37.8818°	89.9818°	0.0431°	1 330
60	45	75	0	53.1301°	90.0000°	0.0191°	3 000
22	46	51	0.0098	25.5547°	90.0283°	0.0620°	924
63	46	78	0.0064	53.8711°	89.9901°	0.0284°	2 020
34	47	58	0.0086	35.8883°	89.9821°	0.0428°	1 338
61	47	77	0.0065	52.3923°	89.9900°	0.0285°	2 013
86	47	98	0.0051	61.3483°	89.9929°	0.0235°	2 443
95	47	106	0.0094	63.6664°	90.0128°	0.0287°	1 993
14	48	50	0	16.2602°	90.0000°	0.0478°	1 200
20	48	52	0	22.6199°	90.0000°	0.0358°	1 600
36	48	60	0	36.8699°	90.0000°	0.0239°	2 400
55	48	73	0	48.8879°	90.0000°	0.0191°	3 000
64	48	80	0	53.1301°	90.0000°	0.0179°	3 200
90	48	102	0	61.9275°	90.0000°	0.0159°	3 600
10	49	50	0.0100	11.5370°	89.9415°	0.1221°	470
25	49	55	0.0091	27.0357°	89.9766°	0.0535°	1 071
38	49	62	0.0081	37.7997°	89.9846°	0.0383°	1 496
50	49	70	0.0071	45.5847°	89.9883°	0.0314°	1 822
67	49	83	0.0060	53.8261°	89.9913°	0.0261°	2 197
94	49	106	0.0047	62.4729°	89.9938°	0.0217°	2 640
10	50	51	0.0098	11.3077°	90.0573°	0.1210°	474
49	50	70	0.0071	44.4270°	89.9883°	0.0314°	1 822
65	50	82	0.0061	52.4369°	89.9912°	0.0262°	2 189
37	51	63	0.0079	35.9658°	89.9848°	0.0381°	1 504
55	51	75	0.0067	47.1666°	89.9898°	0.0287°	1 997
68	51	85	0	53.1301°	90.0000°	0.0169°	3 400
39	52	65	0	36.8699°	90.0000°	0.0220°	2 600
71	52	88	0.0057	53.7862°	89.9922°	0.0241°	2 375
21	53	57	0.0088	21.6183°	89.9743°	0.0594°	964
41	53	67	0.0075	37.7299°	89.9868°	0.0344°	1 666
69	53	87	0.0057	52.4765°	89.9922°	0.0242°	2 368
72	54	90	0	53.1301°	90.0000°	0.0159°	3 600
15	55	57	0.0088	15.2575°	89.9653°	0.0788°	728
24	55	60	0.0083	23.5782°	89.9783°	0.0519°	1 105
40	55	68	0.0074	36.0319°	89.9870°	0.0342°	1 674
48	55	73	0	41.1121°	90.0000°	0.0191°	3 000
51	55	75	0.0067	42.8436°	89.9898°	0.0287°	1 997
75	55	93	0.0054	53.7507°	89.9931°	0.0224°	2 555
31	56	64	0.0078	28.9715°	89.9835°	0.0414°	1 384
33	56	65	0	30.5102°	90.0000°	0.0239°	2 400
42	56	70	0	36.8699°	90.0000°	0.0205°	2 800
73	56	92	0.0054	52.5118°	89.9930°	0.0225°	2 548
90	56	106	0	58.1092°	90.0000°	0.0143°	4 000
97	56	112	0.0045	60.0053°	89.9947°	0.0192°	2 977
44	57	72	0.0069	37.6699°	89.9886°	0.0312°	1 838
76	57	95	0	53.1301°	90.0000°	0.0151°	3 800
87	57	104	0.0096	56.7764°	89.9884°	0.0259°	2 215
79	58	98	0.0051	53.7188°	89.9937°	0.0209°	2 736
43	59	73	0.0068	36.0890°	89.9887°	0.0310°	1 846
77	59	97	0.0052	52.5434°	89.9937°	0.0210°	2 729
11	60	61	0	10.3889°	90.0000°	0.0573°	1 000
25	60	65	0	22.6199°	90.0000°	0.0287°	2 000
32	60	68	0	28.0725°	90.0000°	0.0239°	2 400
45	60	75	0	36.8699°	90.0000°	0.0191°	3 000
63	60	87	0	46.3972°	90.0000°	0.0159°	3 600
80	60	100	0	53.1301°	90.0000°	0.0143°	4 000
91	60	109	0	56.6015°	90.0000°	0.0136°	4 200
47	61	77	0.0065	37.6177°	89.9900°	0.0285°	2 013
83	61	103	0.0049	53.6900°	89.9943°	0.0196°	2 919
81	62	102	0.0049	52.5720°	89.9943°	0.0197°	2 912
16	63	65	0	14.2500°	90.0000°	0.0409°	1 400
46	63	78	0.0064	36.1388°	89.9901°	0.0284°	2 020
60	63	87	0	43.6028°	90.0000°	0.0159°	3 600
84	63	105	0	53.1301°	90.0000°	0.0136°	4 200
95	63	114	0.0088	56.4427°	90.0096°	0.0226°	2 536
23	64	68	0.0074	19.7694°	89.9805°	0.0496°	1 155
33	64	72	0.0069	27.2796°	89.9864°	0.0365°	1 571
41	64	76	0.0066	32.6478°	89.9891°	0.0307°	1 868
48	64	80	0	36.8699°	90.0000°	0.0179°	3 200
87	64	108	0.0046	53.6639°	89.9949°	0.0185°	3 103
20	65	68	0.0074	17.1046°	89.9780°	0.0557°	1 028
26	65	70	0.0071	21.8037°	89.9830°	0.0442°	1 296
50	65	82	0.0061	37.5719°	89.9912°	0.0262°	2 189
72	65	97	0	47.9250°	90.0000°	0.0143°	4 000
76	65	100	0.0050	49.4642°	89.9942°	0.0198°	2 898
85	65	107	0.0047	52.5979°	89.9948°	0.0185°	3 096
88	66	110	0	53.1301°	90.0000°	0.0130°	4 400
29	67	73	0.0068	23.4070°	89.9853°	0.0397°	1 445
49	67	83	0.0060	36.1827°	89.9913°	0.0261°	2 197
91	67	113	0.0044	53.6402°	89.9953°	0.0174°	3 288
44	68	81	0.0062	32.9024°	90.0096°	0.0281°	2 042
51	68	85	0	36.8699°	90.0000°	0.0169°	3 400
80	68	105	0.0048	49.6324°	90.0053°	0.0186°	3 082
89	68	112	0.0045	52.6215°	89.9953°	0.0175°	3 281
53	69	87	0.0057	37.5313°	89.9922°	0.0242°	2 368
71	69	99	0.0051	45.8215°	89.9942°	0.0198°	2 891
92	69	115	0	53.1301°	90.0000°	0.0125°	4 600
24	70	74	0	18.9246°	90.0000°	0.0287°	2 000
70	70	99	0.0051	44.9971°	90.0058°	0.0198°	2 891
95	70	118	0.0042	53.6184°	89.9957°	0.0165°	3 473
17	71	73	0.0068	13.4665°	89.9763°	0.0619°	926
39	71	81	0.0062	28.7822°	89.9897°	0.0301°	1 904
43	71	83	0.0060	31.2030°	89.9906°	0.0279°	2 057
52	71	88	0.0057	36.2215°	89.9922°	0.0241°	2 375
69	71	99	0.0051	44.1844°	89.9942°	0.0198°	2 891
76	71	104	0.0048	46.9509°	89.9947°	0.0186°	3 076
93	71	117	0.0043	52.6431°	89.9957°	0.0165°	3 467
21	72	75	0	16.2602°	90.0000°	0.0318°	1 800
30	72	78	0	22.6199°	90.0000°	0.0239°	2 400
54	72	90	0	36.8699°	90.0000°	0.0159°	3 600
65	72	97	0	42.0750°	90.0000°	0.0143°	4 000
96	72	120	0	53.1301°	90.0000°	0.0119°	4 800
56	73	92	0.0054	37.4952°	89.9930°	0.0225°	2 548
99	73	123	0.0041	53.5985°	89.9960°	0.0157°	3 660
97	74	122	0.0041	52.6630°	89.9960°	0.0157°	3 654
40	75	85	0	28.0725°	90.0000°	0.0191°	3 000
55	75	93	0.0054	36.2563°	89.9931°	0.0224°	2 555
100	75	125	0	53.1301°	90.0000°	0.0115°	5 000
25	76	80	0.0062	18.2100°	89.9849°	0.0424°	1 353
28	76	81	0.0062	20.2233°	90.0135°	0.0384°	1 493
57	76	95	0	36.8699°	90.0000°	0.0151°	3 800
65	76	100	0.0050	40.5416°	89.9942°	0.0198°	2 898
71	76	104	0.0048	43.0544°	89.9947°	0.0186°	3 076
31	77	83	0.0060	21.9313°	89.9880°	0.0349°	1 641
36	77	85	0	25.0576°	90.0000°	0.0205°	2 800
59	77	97	0.0052	37.4629°	89.9937°	0.0210°	2 729
22	79	82	0.0061	15.5627°	89.9835°	0.0466°	1 229
34	79	86	0.0058	23.2877°	89.9893°	0.0319°	1 798
41	79	89	0.0056	27.4306°	89.9912°	0.0273°	2 097
58	79	98	0.0051	36.2875°	89.9937°	0.0209°	2 736
89	79	119	0.0042	48.4087°	89.9959°	0.0158°	3 635
18	80	82	0	12.6804°	90.0000°	0.0358°	1 600
39	80	89	0	25.9892°	90.0000°	0.0191°	3 000
60	80	100	0	36.8699°	90.0000°	0.0143°	4 000
68	80	105	0.0048	40.3623°	90.0053°	0.0186°	3 082
84	80	116	0	46.3972°	90.0000°	0.0119°	4 800
62	81	102	0.0049	37.4337°	89.9943°	0.0197°	2 912
61	83	103	0.0049	36.3156°	89.9943°	0.0196°	2 919
35	84	91	0	22.6199°	90.0000°	0.0205°	2 800
63	84	105	0	36.8699°	90.0000°	0.0136°	4 200
80	84	116	0	43.6028°	90.0000°	0.0119°	4 800
65	85	107	0.0047	37.4073°	89.9948°	0.0185°	3 096
93	85	126	0.0079	47.5694°	90.0072°	0.0183°	3 137
47	86	98	0.0051	28.6587°	89.9929°	0.0235°	2 443
57	87	104	0.0096	33.2352°	89.9884°	0.0259°	2 215
64	87	108	0.0046	36.3412°	89.9949°	0.0185°	3 103
66	88	110	0	36.8699°	90.0000°	0.0130°	4 400
19	89	91	0.0055	12.0515°	89.9831°	0.0506°	1 132
27	89	93	0.0054	16.8773°	89.9881°	0.0368°	1 556
36	89	96	0.0052	22.0243°	89.9911°	0.0287°	1 997
68	89	112	0.0045	37.3832°	89.9953°	0.0175°	3 281
79	89	119	0.0042	41.5954°	89.9959°	0.0158°	3 635
92	89	128	0.0039	45.9514°	89.9965°	0.0143°	4 005
48	90	102	0	28.0725°	90.0000°	0.0159°	3 600
56	90	106	0	31.8908°	90.0000°	0.0143°	4 000
39	91	99	0.0051	23.1998°	89.9919°	0.0266°	2 158
60	91	109	0	33.3985°	90.0000°	0.0136°	4 200
67	91	113	0.0044	36.3645°	89.9953°	0.0174°	3 288
97	91	133	0.0038	46.8297°	89.9968°	0.0137°	4 194
69	92	115	0	36.8699°	90.0000°	0.0125°	4 600
89	92	128	0.0039	44.0521°	89.9965°	0.0143°	4 005
71	93	117	0.0043	37.3612°	89.9957°	0.0165°	3 467
85	93	126	0.0079	42.4233°	90.0072°	0.0183°	3 137
49	94	106	0.0047	27.5333°	89.9938°	0.0217°	2 640
47	95	106	0.0094	26.3208°	90.0128°	0.0287°	1 993
63	95	114	0.0088	33.5477°	90.0096°	0.0226°	2 536
70	95	118	0.0042	36.3859°	89.9957°	0.0165°	3 473
28	96	100	0	16.2602°	90.0000°	0.0239°	2 400
40	96	104	0	22.6199°	90.0000°	0.0179°	3 200
72	96	120	0	36.8699°	90.0000°	0.0119°	4 800
56	97	112	0.0045	30.0000°	89.9947°	0.0192°	2 977
74	97	122	0.0041	37.3410°	89.9960°	0.0157°	3 654
91	97	133	0.0038	43.1736°	89.9968°	0.0137°	4 194
20	99	101	0	11.4212°	90.0000°	0.0318°	1 800
35	99	105	0.0048	19.4712°	89.9917°	0.0280°	2 045
73	99	123	0.0041	36.4055°	89.9960°	0.0157°	3 660
99	99	140	0.0071	45.0029°	89.9942°	0.0157°	3 644
32	100	105	0.0048	17.7438°	90.0090°	0.0302°	1 899
75	100	125	0	36.8699°	90.0000°	0.0115°	5 000
–	–	–	# = 280	–	–	–	–

Checked 9801 combinations

Description:

a, b, c: sides of the triangle

max Δ(a,b,c): desired accuracy of dimensions

Δc: difference between calculated and approximated value of c

α: calculated value of angle α assuming exact dimensions

90°: calculated value of 90° angle assuming exact dimensions

max Δ90°: maximal error of 90° angle

D1(max Δ90°): unity distance at angle (max Δ90°), helps to better understand small angles size

For example enter 2 ≤ a ≤ 100, 2 ≤ b ≤ 100, and max Δ of 0.01. Suppose dimensions are in centimeters, so accuracy of 0.1mm is quite good. Sort by max Δ90° descending ↓

Look at the results. First result (3,4,5) is an Pitagorean triple, but due to dimension deviation of 0.1mm, the maximum 90° angle error is 0.2873°, that's a pretty big error. This can be visualised as 1 meter viewed form 200 meters (or 1 centimeter viewed form 200 cm).

Better results are for triples (6,8,10) and (5,12,13) → max error equals 0.1434°.

It is interesting that triples (10,49,50) and (10,50,51) which do not satisfy the equation a²+b²=c², gives smaller maximum angle error than next Pitagorean triples (9,12,15) and (8,15,17).

This is because of the bigger values of a, b and c in this case, so relative accuracy is better.

As you can see in the table, there are surprisingly many non-Pitagorean triples, which can nevertheless be used as the lengths of the right triangle sides.

In the length range 2-200 the best results are given by the Pythagorean triple (180,189,261), but the triple (189,197,273) is only slightly worse.

Of course, the 90° angle error decreases with increasing dimensions and increasing accuracy (smaller Δ).

Knowing the effects of dimensional errors, we can optimally select the lengths of the triangle sides according to the required accuracy.