My primary question is: If you put a tetrahedron inside a sphere in such a way that the four points of the tetrahedron are on the surface of the sphere, what would be the lattitude on the sphere that the three points at the base of the tetrahedron would share. I could calculate this myself but I don't know the required formulas so here are some other questions about the formulas.

I know that the surface formula for a sphere equals 4*p*r2. Is p the length of the perimeter (equator)?

What are the formulas for angle and line length when we get into the third dimension.

I'm not a mathematician. I'm a sci-fi author and these answers and formulas will help me with a book that I'm writing.