What coordinate system is used in the spherical law of cosines?

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spherical law of cosines is the formula used to calculate the distance between two points on the earth. I've been looking for a reference that discuss about the coordinate system is used in that formula, but no one has discussed what the coordinates systems used by the formula. can anyone help me please???

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http://en.wikipedia.org/wiki/Spherical_trigonometry

Under Cosine rules & sine rules look under Derivation of the cosine

They use the cartesian coordinate system for their proof. They target the distance between points B & C defined by the dot product of dot(b, c) = |b|*|c|*cos a, but given that they're unit vectors with both vectors b & vector c being of length 1, that equates to dot(b, c) = 1 * 1 * cos a => dot(b, c) = cos a. Positions of vector B & vector C are determined using the cartesian coordinate system to determine that angle a representing the distance, just follow the proof.