A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Fleming
Date: 2017 Jul 19, 13:46 -0700
Not sure I followed the problem you would like to solve but I think you are overlooking some information required in your problem.
As you say, given two points on a sphere in lat lon coordinates, you can easily calculate distance between them using Law of cosine formula. Also using that same formula you can calculate other internal angles in the navigational triangle.
To go from one point, a specified distance and reach another point, you must pick which great circle you want to travel along. That is what is the Azimuth of the great circle at the given point. Then the problem of what are the coordinates at the second point is solved using the same formulas as in the first problem.
It is not a one way solution if you supply enough requirements to define the problem.