I have found an image that shows my problem pretty well. At the top, you can see a single phere stacked ontop of three other ones. Let's say the radius of all the spheres is a. I would like to calculate the height of a pyramid consisting of 4 such spheres, but I am completely lost how to do it. I tried applying pythagoras theorem on the spheres, but I can't find any way that works.
HINT
Four spheres are arranged in such way that their centers form a tetrahedron.