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Question: The law of sines for a triangle with angles A, B, and C opposite sides with the respective lengths a, b, and c takes the form

(a/sin A) = (b/sin B) = (c/sin C)

Prove this by considering a vector triangle with sides a, b, and c, where c = a + b, and taking the cross product of c = a + b first with a, then with b, and finally with c.

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