A while ago, I came across a mathematics problem involving the calculation of the length of one side of a triangle, given the internal angles and the lengths of the other two sides. Eventually, after working through the trigonometry of it (which I have now forgotten, but could re-derive if I had to), I realised that it incorporated Pythagoras’ Theorem, but with an extra term based on the cosine of one of the angles. The cosine of 90 degrees is zero, so in a right-angled triangle, this extra term disappears, leaving Pythagoras’ Theorem as usual.
The older law that I knew turned out to be a special case of the more general law.
A while ago, I came across a mathematics problem involving the calculation of the length of one side of a triangle, given the internal angles and the lengths of the other two sides. Eventually, after working through the trigonometry of it (which I have now forgotten, but could re-derive if I had to), I realised that it incorporated Pythagoras’ Theorem, but with an extra term based on the cosine of one of the angles. The cosine of 90 degrees is zero, so in a right-angled triangle, this extra term disappears, leaving Pythagoras’ Theorem as usual.
The older law that I knew turned out to be a special case of the more general law.