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Apply the Law of Cosines

Apply the Law of Cosines. Notes 25 – Section13.6. Essential Learnings. Students will understand the Law of Cosines. Students will be able to apply the Law of Cosines to solve problems involving triangles. Law of Cosines. Used to solve triangles when you know:

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Apply the Law of Cosines

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  1. Apply the Law of Cosines Notes 25 – Section13.6

  2. Essential Learnings Students will understand the Law of Cosines. Students will be able to apply the Law of Cosines to solve problems involving triangles.

  3. Law of Cosines Used to solve triangles when you know: - Two sides and the included angle (SAS) - Three sides (no angles) (SSS)

  4. Law of Cosines - SAS If ∆ABC has sides of length a, b and c as shown, then: SAS – Solve for the side opposite the given angle. Then find the angle opposite the shortest side!

  5. Law of Cosines - SSS Always find the angle opposite the longest side first!

  6. Solving Using Law of Cosines Use the Law of Cosines once, then use the Law of Sines to solve the rest of the triangle.

  7. Example 1 SAS Solve ∆ABC with B = 26, a = 7, c = 12. C 7 26 12 B A

  8. Example 2 SAS Solve ∆ABC with A = 77, b = 15, c = 13. B 13 77 A C 15

  9. Example 3 SSS Solve ∆ABC with a = 7, b = 13, c = 9. Longest side is b – find B first B 9 7 A C 13

  10. Example 4 SSS Solve ∆ABC with a = 23, b = 18, c = 20. Longest side is a – find A first C 18 23 A B 20

  11. Assignment p. 892: 3 – 18 (x3), 37 WS 4 – Applying Law of Sines & Cosines Unit Study Guide 7 – Due next class Unit 8 Test – Tuesday/Wednesday

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