You dont need a tee , unless the pipe you mention is for a sink or something, and you need more means of waste removal i.e sink dishwasher etc.
You said pipe comes up 20''?
So get a 40mm elbow or tee, whatever you need, either push fit or solvent weld,
Cut the pipe lower down, by siting the stand trap next to the pipe, then you'll know how far to cut it back, so the trap fits neatly off the floor, leaving enough space to get hose into top of stand pipe.
The pipe you cut off, use some of it to connect new elbow to elbow on stand pipe, by either glue it or push fit.
That way your materials list wont include new 40mm pipe!
A few holes for clips and your done.