We have a square - find alpha ?
Rotate triangle AEB about B, until A rests on C.
Label the new position of "E" as "G".
Draw a line from E to G.
Angle EBG is 90 degrees.
Angles BEG and BGE are 45 degrees.
Use Pythagoras' Theorem to calculate |EG|
Triangle ECG now has all 3 sides (if you let |AE|=1, |EB|=2, |EC|=3)
and you rearrange the law of cosines to calculate "alpha-45" degrees
and therefore "alpha".