Suppose 2 cases:
Situation 1) I have 2 points, one at (0,0,0) and other at (x, y, z) at a distance d
Situation 2) I have 2 points, one at (0,0,0) and other at (x', 0, z') at a distance d.
How could I get an expression for x' and z' as a function of alpha angle (see Example attached) maintaining the distance d of both points.
This essentially means the two points lie on the sphere centered at the origin, with radius $d$. i.e. $$x^2+y^2+z^2=(x’)^2 +(z’)^2 $$ Any pair $(x’,z’)$ which satisfies this equation will be good to go, the solution is not unique.