Using the law of cosines and a spreadsheet, I identified many simple triangles which share an angle. In the list below, I give the sides of Triangle A and Triangle B, their shared angle, and the cosine of that angle. Tri A Tri B Shared Angle Cos(A) Tri C 4 4 7 1 2 2 28.95502437 7/8 2 3 4 3 3 5 5 7 9 33.55730976 5/6 5 8 9 3 3 4 4 7 9 48.1896851 2/3 7 8 9 1 3 3 3 8 9 19.18813645 17/18 3 5 7 3 7 8 21.7867893 13/14 3 6 7 4 7 9 25.2087653 19/21 3 4 6 4 8 9 26.38432975 43/48 5 5 8 3 4 5 36.86989765 4/5 3 5 7 5 7 8 38.2132107 11/14 5 6 9 2 3 3 38.94244127 7/9 2 2 3 4 5 6 41.40962211 3/4 4 5 7 5 6 7 44.4153086 5/7 2 3 4 6 7 8 46.56746344 11/16 2 5 6 4 4 5 51.31781255 5/8 3 4 5 5 5 6 53.13010235 3/5 2 8 9 6 6 7 54.31466529 7/12 4 5 6 8 8 9 55.77113367 9/16 3 6 7 7 8 9 58.41186449 11/21 3 7 8 5 7 8 60 1/2 4 7 7 7 8 9 73.3984504 2/7 1 2 2 6 7 8 75.52248781 1/4 2 5 5 5 6 7 78.46304097 1/5 2 7 7 5 7 8 81.7867893 1/7 1 4 4 4 5 6 82.81924422 1/8 2 9 9 3 3 4 83.62062979 1/9 1 5 5 5 8 9 84.26082952 1/10 1 8 8 4 6 7 86.4166783 1/16