The case of these triangles is special and close to the Pythagorean theorem, namely $c^2=a^2+b^2\pm ab$. This is a particular case of trigonometric relations and the law of cosines, and remains quite easy without it, using similar triangles and a few tricks. 

So my question is: is it known when this result was studied/written for the first time and was it long before the study of trigonometry? I think it would be strange if it has not been found before understanding the general case. This question was first asked on [Math Stack Exchange](https://math.stackexchange.com/questions/3946854/triangles-with-angle-of-60-degrees-and-120-degrees).