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5.6 Law of Cosines

5.6 Law of Cosines. HW: Pg. 494 #2-20e. Deriving the Law of Cosines. Law of Cosines. Solving a Triangle (SAS). Solve ∆ABC Given: a = 11, b =5, and C = 20°. Solving a Triangle (SSS). Solve ∆ABC Given: a = 9, b =7, and c = 5. Area of Triangle. ∆Area =. C. b. a. A. B. c.

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5.6 Law of Cosines

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  1. 5.6 Law of Cosines HW: Pg. 494 #2-20e

  2. Deriving the Law of Cosines

  3. Law of Cosines

  4. Solving a Triangle (SAS) • Solve ∆ABC Given: a = 11, b =5, and C = 20°

  5. Solving a Triangle (SSS) • Solve ∆ABC Given: a = 9, b =7, and c = 5

  6. Area of Triangle • ∆Area = C b a A B c

  7. Area of Triangle 1/2bcsinA = 1/2acsinB = 1/2absinC

  8. Finding the area of a regular polygon • Find the area of a regular octagon (8 equal sides and angles) inscribed inside a circle of radius 9 inches.

  9. Theorem - Heron’s Formula • Let a,b, and c be the sides of ABC, and let s denote the semiperimeter (a + b + c)/2. Then the area of ABC is given by : Area = √(s(s - a)(s - b)(s - c))

  10. PROOF: Area = 1/2absinC

  11. Using Heron’s Formula • Find the area of a triangle with sides 13, 15, 18.

  12. Measuring a baseball diamond • The bases on a baseball diamond are 90 feet apart, and the front edge of the pitcher’s rubber is 60.5 feet from the back corner of home pate. Find the distance from the center of the front edge of the pitcher’s rubber to the far corner of first base.

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