I'm trying to solve triangulation problems using geographic coordinates from a GPS. all calculations must use the spherical earth model (great circle distance). Given the points and lengths:
Point $A$: N 38 38.000 W 90 20.000
Point $B$: N 38 39.000 W 90 21.000
Line $a$: 4,500 ft.
Line $b$: 4,000 ft.
Line $c$: 7,710 ft. (calculated using great circle distance)
What are points $C$ and $D$ such that $I$ form $2$ triangles?
Sorry for my shoddy paint work, map not drawn to scale