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Law of Cosines: Derivation, Triangles, and Applications

Learn about deriving the Law of Cosines, solving triangles using SAS and SSS, triangle area using Heron's formula, and various applications of the Law of Cosines.

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Law of Cosines: Derivation, Triangles, and Applications

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  1. 5.6 Demana, Waits, Foley, Kennedy The Law of Cosines

  2. What you’ll learn about • Deriving the Law of Cosines • Solving Triangles (SAS, SSS) • Triangle Area and Heron’s Formula • Applications … and why The Law of Cosines is an important extension of the Pythagorean theorem, with many applications.

  3. Law of Cosines Pythag thrm-ish Angle & Side opp are at the ends

  4. Example: Solving a Triangle (SAS)

  5. Solution

  6. Solution

  7. Area of a Triangle Find the area of a triangle with sides 10, 12, 14.

  8. Solution Find the area of a triangle with sides 10, 12, 14.

  9. The figure shown is three mutually tangent circles, with a triangle whose vertices are at the midpoint of each circle. The radii of circles A, B and C are 6, 8 and 12. What is the area of the shaded region?

  10. Homework Page 447; 1 - 34

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