I have a sphere with some latitude parallels in its northern hemisphere. I know the radius of the sphere, and I know the radius of each of the latitude parallels. I also know the distance between all of the parallels.
The problem is, I can't find a correct method of determining the actual latitude values of the parallels.
Another way of looking at this is to say, what is the radius of a given circle of latitude?
Looking at a cross-section of the sphere by a plane through the axis through the poles shows that the radius of the parallel of latitude $\phi$ is $$r = R \cos \phi,$$ where $R$ is the radius of the sphere. Equivalently, $$\phi = \pm \arccos \frac{r}{R} .$$