If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square

Here we apply the Pythagorean theorem:

c^2=a^2+b^2

The diagonal of the opening will be:

c^2=3^2+3^2

c^2=9+9

c^2=18

c=3√2 ft

The diagonal of the wood will be:

c^2=4^2+8^2

c^2=16+64

c^2=80

c=4√5 ft

The space will not be enough for the plywood to pass