My idea:
1) if triangle is right, answer is obvious)
2) if triangle is equilateral, there is no solution
3) in other cases try to split the triangle into 2 right triangles to get coordinates
Correct me if I'm wrong or give test which fail that algo.

17,65,80
result:
0 0
33 -56
48 -64
Edited by author 18.07.2019 20:22

Edited by author 18.07.2019 20:25

Edited by author 18.07.2019 20:26