1) Right click quake 3 arena.
2) Click Properties
3) press local files
4) Click browse local files
5) open folder baseq3
6) open q3config
7) change seta r_customheight to ''1080''
8) change seta r_customwidth to ''1920''
9) change seta r_mode to ''-1'' (<-- minus 1 not underscore)
10) save and exit

Now quake 3 arena will be played in 16x9 in 1920x1080

Known problems so far...
1) fmv and cut scenes no longer play
2) menu and character select models are slightly deformed


Thank you for reading and enjoy quake 3 arena in full HD