How do you derive and apply the law of cosines to solve non-right triangles, especially when given one angle and two sides?

The Law of Cosines is derived from the Pythagorean theorem and is used to solve non-right triangles. It states that for any triangle with sides a, b, and c, and angle C opposite side c: c^2 = a^2 + b^2 – 2ab*cos(C). To solve a triangle given one angle and two sides, use this formula to find the unknown side, then apply the Law of Sines or other trigonometric principles to find the remaining angles and sides.

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