From: horst.kraemer@snafu.de (Horst Kraemer) Subject: Re: Calculating position from angles Date: Sat, 20 Mar 1999 09:12:32 GMT Newsgroups: sci.math On Thu, 18 Mar 1999 13:46:52 +0100, Maurice van der Pot wrote: > Horst Kraemer wrote: > > On Wed, 10 Mar 1999 16:59:18 +0100, Maurice van der Pot > > wrote: > > > I have three points at known coordinates and another point X of which > > > don't know the position. I do know the angles of the three known points > > > as seen from the position of X, but these angles are relative to > > > eachother. > > > How can I calculate the position of X? > > In the plane the problem would be overdetermined. > It would?? Would you care to explain to me why it is overdetermined? Assume a triangle ABC and the angles c=angle(AXB) and a=angle(BXC) given. The locus of all points X such that angle(AXB)=c is a circular segment limited by A and B (THALES) or a double circular segment in case c=pi/2. The same is true for BXC. The intersection of these segments adjacent at B is either no point or one point or a circular segment (B is excluded). The third angle would be either redundant or contradictory except for one single degenerate case. Regards Horst