take a circle with the radius r and its center at (0, 0). If I have two points, A and B of which A is known and B is unknown, how can I calculate the position of B, if I know the distance on the circumference between the two Points?
in my visualisation, if I know A and h, how can I calculate B?
There is not a unique point which has the same distance from $\rm{A}$ as $\rm{B}$. So, you can find two points, say $\rm{B'}$ and $\rm{B''}$, such that $|\overline{\rm{AB'}}|=|\overline{\rm{AB''}}|$. Thus, we have the isosceles triangle $\rm{AB'B''}$, you know both its sides and the vertex between them.
Another way to see this problem is to find the common solutions of the two circles centered in $\rm{O} \equiv (0,0)$ and $\rm{A}$, having radius equal to $|\overline{\rm{OA}}|$ and $|\overline{\rm{AB'}}|$, respectively.
$ \phi_A $ slope at A is known. If $\theta $ is subtended at center by arc $AB =L, $ then
$$ \phi_B =\phi_A \pm \theta = \phi_A \pm \frac{L}{r}.$$
