Hansen's problem

Hansen's problem is a problem in planar surveying. There are two known points A and B, and two unknown points P1 and P2. From P1 and P2 an observer measures the angles made by the lines of sight to the other three points. The problem is to find the position of P1 and P2. (See figure; the angles measured are $\alpha _{1},\beta _{1},\alpha _{2},\beta _{2}$).

Since it involves observations of angles made at unknown points, the problem is an example of resection (as opposed to intersection). It is named after the astronomer Peter Andreas Hansen (1795-1874), who worked on the geodetic survey of Denmark.