Trying to triangulate from two (or three) known points.

Question

If I'm at an unknown location, but I have visible points (monuments) that I know the location of, and I can measure the angle between them, I should be able to determine my location. I'm thinking that with only two monuments, I can narrow my location down to 4 possible points but it seems that once add a third, I should be able to pinpoints my location. I can get a very accurate read on the relative angles between them and know the coordinates of the monuments exactly. Can anyone help?

Answer 1

You are basically correct, although I think if you have two monuments then you have narrowed it down to two locations (one on either side of the two monuments). Knowing a third helps as long as these points are not colinear.

Answer 2

The locus of points for which the angle between the monuments is fixed is a circle. If you have three monuments, you have three pairs, and thus three circles, which all intersect at your location.