Cleaning out old files: in 1978 I used an SR-52 to find scalene
triangles with integral sides and integral areas that were not the sum
or difference of Pythagorean right triangles. Then I noted that the
20 53 55 could be joined to the 20 70 78 to form the 53 78 125 triangle also in this set. Further, the 41 50 89, the 17 40 41 and the 17 55 60 can be joined to make the 60 89 145. By exact cosines the angles seem to match, but maybe I erred or overlooked something.
If correct, it seems kind of neat, but there are probably an indefinite number of these kinds of combinations as the numbers increase. Are these the smallest examples? Brief Internet searching gave me nothing. Does anyone know of any more formal studies done in this esoteric arena?