Complete novice about wireless setup/use.

I need a yes/no answer as to if what I want to do will work and if yes then what is the term for the setup so I can search for some information.

I have a desktop pc connected by ethernet cable to a Modem/router/switch that came bundled with our connection. It has 802.11 b,g, and n capability but wireless is currently switched off.

I want to set up a pc in an outbuilding (20 metres, line of sight) and have another spare modem/router/switch (802.11 b,g) The pc has an ethernet card.

Can I connect the second modem to the second pc and use this to access the first modem wirelessly to get access to the internet ... ?

(otherwise I may have to dig a trench and do some cabling for wired access )