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Grade 10 Math Lab: Proof & Generalization FREE
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Law of Cosines
Learning Objectives
- Solve non-right triangles
- Find unknown sides and angles
- Apply to real problems
Key Concepts
Law of Cosines
c² = a² + b² - 2ab·cos(C)
SSS & SAS
Cases where Law of Cosines is needed
Theory
**c² = a² + b² - 2ab·cos(C)**
**Use when you have:**
- SAS: Two sides and the included angle
- SSS: All three sides (find an angle)
**To find angle:** cos(C) = (a² + b² - c²) / (2ab)
**Note:** Reduces to Pythagorean theorem when C = 90° (cos 90° = 0).
Examples
a=5, b=7, C=60°, find c
Solution: c² = 25 + 49 - 70·cos(60°) = 74 - 35 = 39. c = √39 ≈ 6.24