Both of the above posts offer an accurate assessment of the workings of an RV A/C unit and the electrical requirements. Unfortunately, they are centered around running a 13.5K BTU unit. The OP is asking about a 15K BTU unit and his household branch circuit.
IMO, it's risky to run these high amperage devices on an unknown rated circuit. In most cases the RV owner will be connected into a garage circuit and those can vary by standards at that location and age of house. In my area, an unfinished garage will have 20 amp GFCI protected branch circuits and hopefully, will be separated from other house receptacles. That isn't always the case. If the garage is finished in the interior, 15 amp circuits are allowed. Another intrinsic installation method is that a builder may pull 20 amp wiring throughout the garage but will install 15 amp receptacles to save time and money. I see many of these installations.
An owner should be mindful of exactly what he has regarding the circuit he wishes to use to power the RV. I'd suggest to the OP that he should establish a 50 amp receptacle as close as possible to his new TT. This can be complex as new AWG 6 needs to be pulled back to the load center in the house but will be less risk than trying to run a 15K BTU A/C through an unknown branch circuit. The price of A/C replacement would be more than the 50 receptacle installation.
FWIW, my TT has 50 amp service. I installed a 50 amp receptacle in the garage. Since I had previously installed a subpanel for a welder with 75 amp service, it was easy to add an additional breaker and pull wire for a dedicated 50 amp receptacle for the TT.
Good luck to the OP and hopefully, this discussion helps out with his questions.