Subject: Mathematics
Book: Maths Mastery
The Law of Cosines extends the Pythagorean theorem to non-right triangles: c² = a² + b² – 2ab cos(C), where C is the angle opposite side c. If you know two sides and the included angle, you can find the third side; or if you know three sides, you can find an angle. For instance, if a=7, b=5, and angle C=60°, then c² = 7² + 5² – 2×7×5×cos(60°)= 49 + 25 – 70×0.5=49 + 25 – 35=39, so c=√39. This formula solves oblique triangles, essential in astronomy, land surveying, or advanced geometry proofs. Grasping the Law of Cosines complements the Law of Sines to solve any general triangle scenario.
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