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Law of Cosines a 2 = b 2 + c 2 - 2bc·cos(A)

38 mm. (1) What angles do we cut to create the quadrilateral for this part?. Law of Cosines a 2 = b 2 + c 2 - 2bc·cos(A). 142mm. (2) What is the area of the quadrilateral this part is made from?. 164mm. 122mm. 75 mm.

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Law of Cosines a 2 = b 2 + c 2 - 2bc·cos(A)

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  1. 38 mm (1) What angles do we cut to create the quadrilateral for this part? Law of Cosinesa2 = b2 + c2 - 2bc·cos(A) 142mm (2) What is the area of the quadrilateral this part is made from? 164mm 122mm 75 mm

  2. Law of Cosinesa2 = b2 + c2 - 2bc·cos(A) B a c C b A

  3. The Engineer’s Proof:

  4. The Engineer’s Proof:

  5. The Engineer’s Proof: x - c

  6. The Engineer’s Proof:

  7. The Engineer’s Proof:

  8. The Engineer’s Proof:

  9. The Engineer’s Proof:

  10. The Engineer’s Proof:

  11. The Engineer’s Proof:

  12. SAS? Use Law of Cosines • No Law of Sines ratios available

  13. SAS? Use Law of Cosines • No Law of Sines ratios available • c2 = 702 + 552 -2(70)(55)cos(38o) • c2 = 1,857.317 • c = 43.0967

  14. Now what?

  15. What about this SSS triangle?

  16. Let’s draw a few . . . Then solve.

  17. Heron’s Formula for Area • Let , then

  18. More Applications !!!

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