I'd imagine that they use congruent triangles. If the moon is at its zenith and at the equator, you can know how far away it is horizontally, based on the radius of earth and your position. You can then measure how long the shadows are relative to the objects that cast them, and apply that ratio to the moon's horizontal position to find its height. A good way to test the FET would be to preform similar geometrically sound experiments from different angles, and see if the results are consistent. I haven't seen anyone do this, though.