The basis of a regular pyramid is "a". Perpendicular plane which crosses the centres of two basis, forms smaller pyramid which volume is V.

Declare the followings through "a" and "V":

1)the height of the bigger pyramid

2)the angle between the side edge and base

The answers:

1)h=[64*V*sqrt(3)]/[3*a^2]

2)arctan[64*V]/[a^3]