It's been so long that I barely remember the details, but yes, we used a gnomon to calculate several things... the earth's circumference, our local solar noon, latitude and longitude, etc.
I specifically remember that we measured how far the shadow moved over time using chalk. I think this was in lieu of having a second triangle somewhere else, although, for all I know we might have used a second reference distance.
Our campus had this elaborate outdoor "observatory" that had all sorts of interesting features. The gnomon was one of them, but there were other cool things, like IIRC there was a metal sculpture where Polaris would be seen through a central hole (and a guide inscribed in the concrete to figure out where to stand for that to happen -- I think it was based on viewing height).
Was it the stick on the earth and measuring the right triangle casted by the shadow?
IIRC you also had to do the same thing on another spot far apart and measure the difference between both triangles. At the same time.