Solve triangles given SSS (all three sides) or SAS (two sides and the included angle) using a² = b² + c² − 2bc·cosA. Find all angles, remaining sides, and area.
a² = b² + c² − 2bc·cosA
cosA = (b² + c² − a²) / (2bc)
Area = ½·b·c·sinA
SAS: plug b, c, and A into a² = b² + c² − 2bc·cosA to find a, then use Law of Sines or Cosines for B and C. SSS: use cosA = (b²+c²−a²)/(2bc) to find each angle. Always verify A + B + C = 180°.
The Law of Cosines reduces to the Pythagorean Theorem when A = 90°: a² = b² + c² − 0 = b² + c².
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