when was written for the first time the special relation between sides in a triangle with an angle of $60$ degrees or $120$ degrees ?

This question was first asked here:

https://math.stackexchange.com/questions/3946854/triangles-with-angle-of-60-degrees-and-120-degrees

So this is a particular case of trigonometric relations and law of cosines; I think it would be strange that it has not been found before understanding the general case. Thanks in advance for your comments.

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.

when was written for the first time the special relation between sides in a triangle with an angle of $60$ degrees or $120$ degrees ?

This question was first asked here:

https://math.stackexchange.com/questions/3946854/triangles-with-angle-of-60-degrees-and-120-degrees

So this is a particular case of trigonometric relations and law of cosines; I think it would be strange that it has not been found before understanding the general case.

when was written for the first time the special relation between sides in a triangle with an angle of $60$ degrees or $120$ degrees ?

This question was first asked here:

https://math.stackexchange.com/questions/3946854/triangles-with-angle-of-60-degrees-and-120-degrees

So this is a particular case of trigonometric relations and law of cosines; I think it would be strange that it has not been found before understanding the general case. Thanks in advance for your comments.