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I'm trying to solve triangulation problems using geographic coordinates from a GPS. all calulations 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

![map]: http://i.imgur.com/KfOU3.png

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