Most likely, you are ok.
Exactly which cooler are we talking about?
A Noctua NH-D14 or phanteks are about the best air coolers at <$100. They are about 160mm tall which will fit in your 180mm wide case. Google the cooler and case, and you will likely find pics to show you how it fits.
If you are talking about a $100 all in one liquid cooler(which I do not recommend), then the radiator size may be an issue.