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Pythagorean Theorem

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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:

 

a2 + b2 = c2,     sqrt[a2 + b2] = c,    

 

0 <= c - b <= a      <= b
0 <= c - b <= c - a <= b <= c <= a + b
0 <= b - a <= c - a <= b

 

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:
A is the angle opposite side a and adjacent to sides b and c.
B is the angle opposite side b and adjacent to sides a and c.

 

The angles A and B satisfy the following:
A=sin-1(a/c)=cos-1(b/c)=tan-1(a/b).
B=sin-1(b/c)=cos-1(a/c)=tan-1(b/a).
A+B=90 degrees.

 

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)
34536.953.1
5121322.667.4
7242516.373.7
8151728.161.9
9404112.777.3
11606110.479.6
12353718.971.1
1384858.881.2
151121137.682.4
16636514.375.7
171441456.783.3
191801816.084.0
20212943.646.4
209910111.478.6
212202215.584.5
232642655.085.0
241431459.580.5
253123134.685.4
273643654.285.8
28455331.958.1
281951978.281.8
294204213.986.1
314804813.786.3
322552577.282.8
33566530.559.5
335445453.586.5
356126133.386.7
36778525.164.9
363233256.483.6
376846853.186.9
39808926.064.0
397607612.987.1

 

a
(memorize)
b
(memorize)
c
(memorize)
A in degrees
(memorize)
B in degrees
(memorize)
403994015.784.3
418408412.887.2
439249252.787.3
4411712520.669.4
444834855.284.8
48557341.148.9
485755774.885.2
5114014920.070.0
5216517317.572.5
526756774.485.6
567837854.185.9
5717618517.972.1
609110933.456.6
6022122915.274.8
608999013.886.2
65729742.147.9
6828529313.476.6
6926026914.975.1
7530831713.776.3
7635736512.078.0
8418720524.265.8
8443744510.979.1
8513215732.857.2
8741642511.878.2
8810513740.050.0
925255339.980.1
9347648511.178.9
9516819329.560.5
9624726521.268.8

 

a
(memorize)
b
(memorize)
c
(memorize)
A in degrees
(memorize)
B in degrees
(memorize)
1006216299.180.9
10415318534.255.8
10520823326.863.2
1056086179.880.2
1087257338.581.5
1116806899.380.7
11525227724.565.5
1168378457.982.1
11912016944.845.2
12020924129.960.1
12039140917.172.9
1238368458.481.6
1249579657.482.6
1299209298.082.0
13247549315.574.5
13315620540.449.6
13535237721.069.0
13627330526.563.5
14017122139.350.7
14540843319.670.4
15234537723.866.2
15546849318.371.7
15666768513.276.8

 

a
(memorize)
b
(memorize)
c
(memorize)
A in degrees
(memorize)
B in degrees
(memorize)
16023128134.755.3
16124028933.956.1
16553255717.272.8
16842545721.668.4
16877579312.277.8
17528833731.358.7
18029934931.059.0
18451354519.770.3
18567269715.474.6
18934038929.160.9
19574877314.675.4
20060964118.271.8
20339644527.162.9
20425332538.951.1
20582885313.976.1
20722430542.747.3
21591293713.376.7
21671374516.973.1
21745650525.464.6
22045950925.664.4
22527235339.650.4
22832539735.154.9
23152056924.066.0
23282585715.774.3
24055160123.566.5
24894597714.775.3
25227537342.547.5
25966070921.468.6

 

a
(memorize)
b
(memorize)
c
(memorize)
A in degrees
(memorize)
B in degrees
(memorize)
26065170121.868.2
26138046134.555.5
27373678520.469.6
27649356529.260.8
27944052132.457.6
28035144938.651.4
28075980920.269.8
28781686519.470.6
29730442544.345.7
30058966127.063.0
30190094918.571.5
30843553335.354.7
31557265328.861.2
31936048141.548.5
33364472527.362.7
33637750541.748.3
33652762532.557.5
34142054139.150.9
34880587723.466.6
36462772530.159.9
36846559338.451.6
36980088124.865.2
37292599721.968.1
38555267334.955.1
38788496523.666.4
39640356544.545.5

 

a
(memorize)
b
(memorize)
c
(memorize)
A in degrees
(memorize)
B in degrees
(memorize)
40056168935.554.5
40762474533.156.9
42085194926.363.7
42946062943.047.0
42970082131.558.5
43266579333.057.0
45178090130.060.0
45552869740.849.2
46477790530.859.2
46859575738.251.8
47386498528.761.3
48160076938.751.3
50470386535.654.4
53375692535.254.8
54062982940.649.4
55557279744.145.9
58074194138.151.9
61572895340.249.8
61666390542.947.1
69669798545.045.0