Question

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1200 kilometers due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 79 ∘.

Answer 1

You know now that 1200 km is 11° of latitude on the planet. So its circumference is roughly approximately around something like about

(360/11) • (1200 km) = 39,273 km

If it was good enough for Eratosthenes, then we can't complain.