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Looks like solvent welded pipe? If the joint that came loose was solvent welded you must have hit it pretty hard. Maybe it was supposed to be solvent but was just pushed in. If that's the case then it's been a problem waiting to happen for a while.
I'm no plumber but have been DIY pipe wrestling over the past few days. If it was mine I would want to get full access for the repair so I could be convinced it was watertight. I say this having just repaired a basin that started leaking in multiple places that were hard to get to.
Yeah sorry, bit of a pointless ask. It's all pretty standard, but as far as I can tell the sink was partially plumbed in before the unit was fitted. The joint that came apart is just below the lower hole, so with one arm under the unit and the other holding the bit in the photo, I rejoined the pieces. It seems like a quick fix would be to drill another hole in the back board, or enlarge the existing one, so I can dab some adhesive on the join and all is well.
Aside from the water under the floorboards, but I really don't want to get into that.