spatial database - Given long, lat, x and y, how do I find the projection?

I am using an app called farsite that outputs shapefiles that show how forest fires will grow. I am getting output in coordinates as X and Y values rather than (lon,lat) and am looking for a conversion routine to (lon, lat). If I knew the name of the coordinate system it might help my search, but I do not even know that. I have gone to google maps and have looked at the expected (lon, lat) so I have a rough translation equation, but I am sure that someone else has a better one (mine is linear with a scale and offset, which I fear is too simplistic)

Here is a sample point (X, Y): 162206 386691 (Lon,Lat): -115.326662 47.582952

Can someone please steer me to a reference or conversion routine?

Thanks in Advance - Steve Tufty

Answer

Looks like Thompson Falls, MT. The current state plane coordinate system (1983) for Montana projects (-115.326662 47.582952) to (162339, 386636), which is (133, -55) meters off: not awful, but not good, either. You could be using a custom datum or maybe your site coordinates are actually off by that much. It's unlikely any other standard coordinate system could produce coordinates in this range.

If this looks right, any software that unprojects state plane coordinates will do the job. There's an online Montana government applet for one-off conversions. Shapefiles are best processed with GIS software.