I had to deal with white pages here last night so I went on to bed. Sorry.
Most instructions for wireless network devices suggest to keep the antenna above your head. I personally follow this guideline even though it would take a life time of exposure to give you a tingle. Besides as Russel can tell you the higher the antenna the greater distance you can cover.
Ok on to figuring out the size of the footprint.
Set it for opposite side and hypotenuse side. In adjacent side put the distance from your antenna to the wall of the school. Keeping in mind that that only figures 1/2 of the beam angle put in 15 for angle. Take the figure for opposite side, multiply it by 2 and that's the beam spread at the target end.
If you figure the distance is 100 feet at 1/2 of the beam angle 15 (half of the lobe) at that distance you'd have a 1/2 beam spread of just over 26 feet. Take 26 multiply by 2 and you get 52 feet. However since the lobe is teardrop shaped, the optimum spread would actually occur at roughly 90 feet. Gets complicated from there.
At any rate, if you need a wider footprint at the target end you'll need to look for a directional antenna that has a wider beam angle. But the wider the angle the less RF energy will arrive at the target. Directional antennas work by focusing the RF energy in one direction. They don't amplify the signal just point it one direction. Where as omni's like what comes on most home wireless wastes the RF energy by radiating in all directions.