As above, the distance between APs is unlikely to be a problem as you mention the site is big, and as @PhilipDAth says with just three APs you can avoid overlapping channels in the 2.4GHz band (I'd set the channel selection to 'auto' and let Dashboard figure things out, it'll factor in other wireless detected.)
Have you a floorplan of the site? Even without using an RF design tool it will make it easier to eyeball the best position to add an AP.
Consider if there're walls/other obstructions likely to block RF, interference sources (other companies' APs, microwave ovens, wireless video senders, industrial equipment etc.).
Have you looked in Dashboard with Air Marshall and RF Spectrum to see how things are?
If it's a benign environment with low density of devices you can probably just stick in an extra AP in the middle of the dead zone, if things are complicated it's worth applying a bit more thought.