Pythagorean Theorem

Pythagorean Theorem

In a right triangle with sides of length 0 <= a <= b <= c,<br>c is the length of the hypotenuse (the side opposite the right angle),
while a and b are the lengths of the legs of the triangle.

 

In such a right triangle, the following hold:

 

 

 

If a, b, c are all positive integers, they form what is called a <b>Pythagorean Triple,
as discussed on http://www.mathsisfun.com/numbers/pythagorean-triples.html

and listed below.

 

Also listed below are the angles A and B in degrees:

 

The angles A and B satisfy the following:

 

The Pythagorean Triples listed below can be used
to build right triangles with the desired angles A and B.

 

You could try to memorize the chart below,
or you could use its contents as practice exercises.

Pythagorean Triples

a (memorize)	b (memorize)	c (memorize)	A in degrees (memorize)	B in degrees (memorize)
3	4	5	36.9	53.1
5	12	13	22.6	67.4
7	24	25	16.3	73.7
8	15	17	28.1	61.9
9	40	41	12.7	77.3
11	60	61	10.4	79.6
12	35	37	18.9	71.1
13	84	85	8.8	81.2
15	112	113	7.6	82.4
16	63	65	14.3	75.7
17	144	145	6.7	83.3
19	180	181	6.0	84.0
20	21	29	43.6	46.4
20	99	101	11.4	78.6
21	220	221	5.5	84.5
23	264	265	5.0	85.0
24	143	145	9.5	80.5
25	312	313	4.6	85.4
27	364	365	4.2	85.8
28	45	53	31.9	58.1
28	195	197	8.2	81.8
29	420	421	3.9	86.1
31	480	481	3.7	86.3
32	255	257	7.2	82.8
33	56	65	30.5	59.5
33	544	545	3.5	86.5
35	612	613	3.3	86.7
36	77	85	25.1	64.9
36	323	325	6.4	83.6
37	684	685	3.1	86.9
39	80	89	26.0	64.0
39	760	761	2.9	87.1

 

a (memorize)	b (memorize)	c (memorize)	A in degrees (memorize)	B in degrees (memorize)
40	399	401	5.7	84.3
41	840	841	2.8	87.2
43	924	925	2.7	87.3
44	117	125	20.6	69.4
44	483	485	5.2	84.8
48	55	73	41.1	48.9
48	575	577	4.8	85.2
51	140	149	20.0	70.0
52	165	173	17.5	72.5
52	675	677	4.4	85.6
56	783	785	4.1	85.9
57	176	185	17.9	72.1
60	91	109	33.4	56.6
60	221	229	15.2	74.8
60	899	901	3.8	86.2
65	72	97	42.1	47.9
68	285	293	13.4	76.6
69	260	269	14.9	75.1
75	308	317	13.7	76.3
76	357	365	12.0	78.0
84	187	205	24.2	65.8
84	437	445	10.9	79.1
85	132	157	32.8	57.2
87	416	425	11.8	78.2
88	105	137	40.0	50.0
92	525	533	9.9	80.1
93	476	485	11.1	78.9
95	168	193	29.5	60.5
96	247	265	21.2	68.8

 

a (memorize)	b (memorize)	c (memorize)	A in degrees (memorize)	B in degrees (memorize)
100	621	629	9.1	80.9
104	153	185	34.2	55.8
105	208	233	26.8	63.2
105	608	617	9.8	80.2
108	725	733	8.5	81.5
111	680	689	9.3	80.7
115	252	277	24.5	65.5
116	837	845	7.9	82.1
119	120	169	44.8	45.2
120	209	241	29.9	60.1
120	391	409	17.1	72.9
123	836	845	8.4	81.6
124	957	965	7.4	82.6
129	920	929	8.0	82.0
132	475	493	15.5	74.5
133	156	205	40.4	49.6
135	352	377	21.0	69.0
136	273	305	26.5	63.5
140	171	221	39.3	50.7
145	408	433	19.6	70.4
152	345	377	23.8	66.2
155	468	493	18.3	71.7
156	667	685	13.2	76.8

 

a (memorize)	b (memorize)	c (memorize)	A in degrees (memorize)	B in degrees (memorize)
160	231	281	34.7	55.3
161	240	289	33.9	56.1
165	532	557	17.2	72.8
168	425	457	21.6	68.4
168	775	793	12.2	77.8
175	288	337	31.3	58.7
180	299	349	31.0	59.0
184	513	545	19.7	70.3
185	672	697	15.4	74.6
189	340	389	29.1	60.9
195	748	773	14.6	75.4
200	609	641	18.2	71.8
203	396	445	27.1	62.9
204	253	325	38.9	51.1
205	828	853	13.9	76.1
207	224	305	42.7	47.3
215	912	937	13.3	76.7
216	713	745	16.9	73.1
217	456	505	25.4	64.6
220	459	509	25.6	64.4
225	272	353	39.6	50.4
228	325	397	35.1	54.9
231	520	569	24.0	66.0
232	825	857	15.7	74.3
240	551	601	23.5	66.5
248	945	977	14.7	75.3
252	275	373	42.5	47.5
259	660	709	21.4	68.6

 

a (memorize)	b (memorize)	c (memorize)	A in degrees (memorize)	B in degrees (memorize)
260	651	701	21.8	68.2
261	380	461	34.5	55.5
273	736	785	20.4	69.6
276	493	565	29.2	60.8
279	440	521	32.4	57.6
280	351	449	38.6	51.4
280	759	809	20.2	69.8
287	816	865	19.4	70.6
297	304	425	44.3	45.7
300	589	661	27.0	63.0
301	900	949	18.5	71.5
308	435	533	35.3	54.7
315	572	653	28.8	61.2
319	360	481	41.5	48.5
333	644	725	27.3	62.7
336	377	505	41.7	48.3
336	527	625	32.5	57.5
341	420	541	39.1	50.9
348	805	877	23.4	66.6
364	627	725	30.1	59.9
368	465	593	38.4	51.6
369	800	881	24.8	65.2
372	925	997	21.9	68.1
385	552	673	34.9	55.1
387	884	965	23.6	66.4
396	403	565	44.5	45.5

 

a (memorize)	b (memorize)	c (memorize)	A in degrees (memorize)	B in degrees (memorize)
400	561	689	35.5	54.5
407	624	745	33.1	56.9
420	851	949	26.3	63.7
429	460	629	43.0	47.0
429	700	821	31.5	58.5
432	665	793	33.0	57.0
451	780	901	30.0	60.0
455	528	697	40.8	49.2
464	777	905	30.8	59.2
468	595	757	38.2	51.8
473	864	985	28.7	61.3
481	600	769	38.7	51.3
504	703	865	35.6	54.4
533	756	925	35.2	54.8
540	629	829	40.6	49.4
555	572	797	44.1	45.9
580	741	941	38.1	51.9
615	728	953	40.2	49.8
616	663	905	42.9	47.1
696	697	985	45.0	45.0