What formula relates rational sides and hypotenuse in spherical geometry?
I obtained an example quite by chance:
$$ \cos \frac{5}{18} \cos \frac{1}{3} = \cos \frac{31}{72} $$
with radius of sphere $72$, sides $(20,24)$ and "hypotenuse" $31.$
.. like we have flat Euclidean sides/hypotenuse geometry using rationals $(m^2-n^2,2mn, m^2+n^2 ).$