using plain/plane geometry i managed to setup three cosine formulas for 2 adjacent triangles, introducing 2 additional auxiliary variables and the

software managed to solve the set of three nonlinear equations, and for a numerical example it produced the same result (

*gap=1.37838cm*) but that was not the way to go, way too complicated. your approach

M
Mr.Wizard
using the complex plane is the most elegant path, of course giving the same numerical result. i had to refresh my basic knowledge on complex pointers

**Z **and then was able to restate your solution:

complex pointers are in many ways "the same" as position vectors in the 2D-plane, so your two "different" approaches are basically the same, unlike my idea of the

Law Of Cosines never mind. anyway, given a set of parameters {

*t, d, R, r, 40°*} it is still not very easy to operate the "simple" formula on a handheld calculator (-> user error

).

and me too, i doht have an original tormek either