1) Using the null of a loop antenna, find a vector to the beacon using
a compass. Note the location where the vector was found on a GPS. Do
this from multiple locations and the beacon is where the lines
intersect. Since there will be error in both the compass (2 degrees
using a Garmin GPS) and some error in finding the null, the result will
be more of a locus of points where the beacon could be located rather
than the beacon itself.
I have posted a law-of-cosines calculation example several times where
coordinates of an intersection point are determined from two GPS locations
with a bearing from each location...to the intersection point. I can find
one of those in my files and post it later if that is needed.
But it could been done graphically with 'Scratch-Plot' because one of the
newer features of 'Scratch-Plot' is a plot by azimuth and distance. Just
set-up a scale of UTM coordinates, plot each GPS location in UTM
coordinates, plot a line from each location with an azimuth direction and a
dummy-distance so that the lines intersect, mouse-click a point at the
intersection of the lines, and check the coordinates of the mouse-click
point immediately in the help file or later in the plot text file.
Here is a user link to 'Scratch-Plot' :
http://www.kbhscape.com/plot.htm
Also, the difference between a geodetic direction and a UTM grid direction
can be determined with 'Geodetic/UTM-Grid Utility' by entering the latitude
and longitudes and comparing geodetic directions to grid directions.
And here is a user link to 'Geodetic/UTM-Grid Utility' :
http://www.kbhscape.com/gps.htm