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Originally posted by pres589 28mm on a crop Pentax is not wide, it's almost perfectly normal, which is why I love 28's on crop.
I would be looking at manual focus primes to try and meet your cost target which I read is $100ish. Sigma Super-Wide II's are around there. The later AF versions go for more.
I have a manual everything RMC Tokina 17mm that you could find for less than $150 on the rare occasions they come up. 17mm on APS-C is wide but easy to manage, it's the cutover between wide and ultrawide for FF. My lens is sharp with great colours and for landscapes you would not be worried by the lack of half-stops in the aperture ring. It is smooth to focus, chunky and metallic in a way that suggests good engineering.
Just a thought, but as you have seen in other comments, the creative options are much better with the 16-45mm which I have also, and I bought mine for $120.