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with reference to Trilateration using 3 latitude and longitude points, and 3 distances.

The accepted answer was votes as shown in wikipedia at: http://en.wikipedia.org/wiki/Trilateration in conjunction with a conversion to Radians before and after.

Is there a way to incorporate Vincenty's formulae http://en.wikipedia.org/wiki/Vincenty%27s_formulae to this process to bring a more accurate answer?

Kind Regards

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Over the sort of distances in the original question, its unlikely to make any kind of significant distance. Can you tell us more about your specific situation? –  BradHards Mar 24 '13 at 10:55
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For a discussion of various problems in ellipsoidal trigonometry, see Sections 10 and 11 of http://arxiv.org/abs/1102.1215

Some similar problems are also discussed in http://dx.doi.org/10.1007/s00190-012-0578-z

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