I had read that for a "spherical" triangle i.e. all sides are equal and all angles are 90 degrees if e.g.
(I am sorry for the crude diagram, didn't know how to make it better)
it is: $\cos s = \cos x \cdot \cos y$
but I am not sure how we come about this.
I think:
$x = s \cdot \cos y$ and $y = s \cdot cos x$ and I assume that we can treat each side as hypotenuse but I can't derive the formula.
I remember that if $x$ and $y$ are very small and we use the series definition for $sin$ and $cos$ and ignoring all $x^2$ and rest terms as very small, we can get $s^2 = x^2 + y^2$ which is the pythagorean theorem.
Is there some way to derive $\cos s = \cos x \cdot \cos y$ from the triangle that I am missing?