There is one more thing to complicate your example. Your example presumes that you know an absolute direction. The problem is that you have nothing to tell you any absolute direction.
In fact, you will have one compass that points at A. All you know about that direction is that it points at A, so you can call the direction A'. The other compass points at B, and the direction is B'. Now is the time to determine your exact point, but your only numerical data is the angle between A' and B', which ends up describing an arc between A and B. (to demonstrate this have someone hold their fingers a handswidth apart and then set the corner of a square object such as a book inbetween the fingers. Now move the point around while touching both fingers with the edge of the book. The point will trace an arc.) You don't have the distance to either A or B. However, given a precise enough compass, you could take your readings, measure the angle, and then travel a day's travel towards a landmark that bisects the angle, and then use that new A2' and B2' in combination with A' and B' to accurately triangulate your position. You would need another datum, such as the direction of true north, in order to triangulate from a single measurement.
No?
+++++++++++++++++++++++23
Powered by hypermail