One of the most popular triangles used in Math, Trig, and Physics problems is the 3-4-5 right triangle. To provide more variety in our problem development here are 17 alternative Pythagorean Triangles where the sides are all integers.

Labeled Pythagorean Triangle

Sample triangle with labels matching Pythagorean Triangle Table.The sides of the triangle are labeled, a and b with the hypotenuse c. The opposite angles are labeled, α, β, and ɣ. — Sample triangle with labels matching Pythagorean Triangle Table.
The sides of the triangle are labeled, a and b with the hypotenuse c. The opposite angles are labeled, α, β, and ɣ.

Table of Pythagorean Triangles

	
   
      Side Length
       
      Vertex Angles (deg)
   

      a
      b
      c
      Area
      alpha
      beta
      gamma
   

      3
      4
      5
      6
      36.67
      53.33
      90
   

      5
      12
      13
      30
      21.77
      68.23
      90
   

      7
      24
      25
      84
      16.04
      73.96
      90
   

      9
      40
      41
      180
      12.03
      77.97
      90
   

      11
      60
      61
      330
      9.74
      80.26
      90
   

      13
      84
      85
      546
      8.02
      81.98
      90
   

      33
      56
      65
      924
      29.79
      60.21
      90
   

      39
      80
      89
      1560
      25.21
      64.79
      90
   

      65
      72
      97
      2340
      41.83
      48.17
      90
   

      8
      15
      17
      60
      27.5
      62.5
      90
   

      12
      35
      37
      210
      18.33
      71.67
      90
   

      16
      63
      65
      504
      13.75
      76.25
      90
   

      20
      99
      101
      990
      10.89
      79.11
      90
   

      20
      21
      29
      210
      42.97
      47.03
      90
   

      28
      45
      53
      630
      31.51
      58.49
      90
   

      36
      77
      85
      1386
      24.64
      65.36
      90
   

      48
      55
      73
      1320
      40.68
      49.32
      90
   

      60
      91
      109
      2730
      32.66
      57.34
      90
   

References

Butler, Douglas. 2004. “Pythagorean Triples.” TSM Resources. http://bit.ly/2m0C43t.

Weisstein, Eric W. 2010. “Pythagorean Triple.” Education. Wolfram MathWorld. August 3. http://bit.ly/2mPRRkL.