You definitely need measurements from two landmarks. With two measurements, you limit the number of points that meet your description to two, and by adding compass directions (or, as Bob suggests, the line of sight), a reasonably competent person can easily eliminate one of them.
A stipulation that the finish line should be set perpendicular to the race route on the last stretch wouldn't hurt, either- although as mentioned in the other thread, we simply make that assumption when a finish line is on a surface with defined sides, and it is far from a stretch to make that assumption here.