That looks like a handsome Kentucky rifle which usually have a barrel length of 33" - 35", having an attractive unitary one piece stock rather than the more common two piece stock that's joined in the middle, and a nicely shaped patchbox.
Is the rifle actually marked .45 or could it be a .44?
Euroarms once made a .44 Kentuckian rifle and also a shorter 27.5" carbine version.
It looks to be a fairly good quality gun that was probably made by a major well known maker.
The barrel appears that it could benefit by being reblued/browned but the stock looks pretty good as it is unless you're really hankering for a refinishing project.
What to do with it could depend on the condition of the bore, how well it shoots and how much that you like it.