What gauge extension cord should I use for a 75-foot air compressor run?

Get the 10/3 cord. A heavy-duty air compressor draws high current, especially on startup, and a 12/3 cord at 75 feet will cause voltage drop that makes the motor struggle, run hot, and risk early failure. The 10/3 is thicker, handles the surge, and is the safe, long-term choice for a several-hundred-dollar tool.