Thanks guys. Yes, 3hp motor is what the advertising says though I haven't purchased yet. And yes, the dryer circuit breaker is in the main service panel on the opposite side of the house as the attached garage.
I took a closer look at trying to determine the actual length of the wire this afternoon and it looks like it's probably closer to 130' or more. The cable goes to the laundry room outlet first and then travels an additional 30' to a second outlet in the garage. House is set up to run a dryer in either the laundry room or the garage, but not both. Will need to connect the wires together at the junction box in the laundry room to make the outlet in the garage hot. Not sure if that should be simple wire nuts or something else?
Then I will need to run another 30' of wire from the garage outlet to the compressor location. It's looking like that will need to be 8 gage as it's at least 160' from the breaker now.
I found someone on here that said the tag indicates 16.6A for this compressor. I think I should still be fine given the increased length.