While creating a perch for our parrot, I stumbled upon something non trivial : if you want to assemble a box with non vertical sides, what cut angle are you supposed to use to have a nice assembly ? It’s obvious that it should be a trapeze, but what would be the α angle ?
Easy peasy, let’s dig into the maths!
On the schematics, once assembly is done, we have B=B’ and A,B, B’, A’ in same plane.
Supposing that we have an angle β with vertical (meaning a standard box has β=0), this means
as OA = OA’, we have trivially
And by the way, why did I need that ? Just to make it real :