I'd be super grateful for some help with this practical question relating to angles and area.
I'm a musician (not a mathematician, sadly) and I'm building a recording studio in my garden. I'm trying to figure out how to get the most out of my space, but need to allow enough room to slide an upright piano in - presumably at a diagonal angle through the entrance and the side door to the left. Please see below pics for studio dimensions and the door layout, and dimensions of the piano.
My questions is, how wide do the entrance door (opening forwards, not shown here) and left door (opening backwards) have to be to allow the piano to safely slide in? I can't think for the life of me how I'm supposed to work this out. Of course I could play it safe and make the entrance doors >153cm wide and then move it orthogonally to the left, but it seems like a waste of space, plus the doors would be massive.
If anyone can provide some clarity on this I'd be eternally grateful. Thank you!
If $L$ is the point where your doors will join and $D$ is the point where your middle wall ends, and 80 cm wide door will be enough to move your piano diagonally, with a margin of safety of at about 1 inch on each side, because the distance from point $A$ to point $C$ will be larger than the 65 cm, since the piano is being moved diagonally.
In my picture I suposed your wall ends about 30 cm from where your doors meet. Hope it helps you.
You can also try moving the piano in my geogebra simulation. I've made so you can also make the doors narrower, remove the middle wall, or rotate the piano by moving the points C, B and D, until you get another pair of 90 degree angles.