Mind Your Decisions - maths fail

It’s length 4 from one corner of a hexagon to the opposite corner.
‘Vertical’ height of each triangle in the hexagon = sq rt 3.
Put the square flat on the table, fold up the flaps and look at it from the side.
Point E/F is 1 ‘across’ and has hypotenuse sq rt 3.
Acos 1/sq rt 3 = 54.74 deg (no need to know length of the other side).

Then rotate the square so that you are looking at it diagonally from one corner.
Distance from E/F to a point diagonally opposite (assuming there are four hexagons all folded up) = 4 x sq rt 2.
Distance diagonally across the square = 2 x sq rt 2.
So point E/F is sq rt 2 ‘across’ and has hypotenuse 2 (side length of hexagon).
Acos sq rt 2/2 = 45 deg (no need to know length of the other side).