In excersise 3.7 from Geometry and Topology by Reid M. and Szendroi B. they ask me to prove that $(p,q,r)$ must have a specific form when you have an acute angled spherical triangle whose angles are submultiples of $\frac{\pi}{p}, \frac{\pi}{q}, \frac{\pi}{r}$.
I cannot find what an acute angle means on a sphere. Is it still that no angle can be more than or equal to $\frac{\pi}{2}$? Because the possibilities for $(p,q,r)$ all have $2$ in their answers, which would mean right angles on a normal triangle (so not acute as the question states), and so now I'm assuming that on spheres it works the same.
Using the hint at the bottom of the excersise and using that the area of a triangle must be greater than 0 gives me that expression, and from there on it's easy to get the triples $(p,q,r)$ for which this holds.
"
"
Since they're using the same word to describe a right triangle in ordinary Euclidean geometry... just replace the word "acute" by "non-obtuse" and move on. It's a bad choice of words, but the meaning is clear. Right angles are allowed in this one.