f the distance between reference points A (for example, the upstream tip of a prominent sand bar) and B (the top of a river bluff) is known, and the angles x and y can be read from compass bearings between B and C (a tall tree on the opposite side of the river) and A and C, then lines can be drawn from A to C and B to C completing a triangle with one known leg (AB) and two legs (BC and AC) that can be estimated with a high degree of accuracy.
This estimation can be done by "scaling." If line AB is 1 mile long in the real world and 10 inches long on the diagram, then the map scale is 0.1 inches to 1 mile; the distance from B to C can be determined by measuring the distance on the diagram and multiplying by the scale (if the diagram distance BC is 6 inches, then real world distance is 6 miles). There are also mechanical ways that the distance estimates could be arrived at, using draftsman's dividers or a similar instrument. The points of the divider could be set 1/10 of an inch apart to represent the diagram scale and the dividers could then be "walked" along line BC to determine its length.
--John Logan Allen