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Mastering the Law of Sines and Cosines in Algebra 2

On May 17, 2011, we focused on reviewing the Law of Sines and practicing the Law of Cosines in our Algebra 2 class. The Law of Sines is a crucial tool for solving triangles by finding missing sides or angles. Remember, angles are designated with capital letters. Through guided practice, students developed skills in applying these laws to various triangle problems, ensuring a deeper understanding of trigonometric relationships.

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Mastering the Law of Sines and Cosines in Algebra 2

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  1. 17 May 2011

    Algebra 2
  2. Agenda: Review Quiz Law of Sines Student Practice Law of Cosines Student Practice
  3. Law of Sines 5/17 The Law of Sines can be used to find missing sides or angles in a triangle. Angles (corners) are labeled with a CAPITAL letter. Sides (lines) are labeled with lower-case letters. Introduction
  4. Law of Sines 5/17 Angles A CB Introduction
  5. Law of Sines 5/17 Sides A bc CaB Introduction
  6. Law of Sines 5/17 Notice: A bc CaB Introduction
  7. Law of Sines 5/17 Notice: A bc CaB Introduction
  8. Law of Sines 5/17 Notice: A bc CaB Introduction
  9. Law of Sines 5/17 The Law of Sines states: Definition
  10. Law of Sines 5/17 Verify the Law of Sines: A 50o b = 12.46c = 11 57.42o 72.58o Ca = 10B Introduction
  11. Find the indicated side: A 50o b = ? 70o Ca = 12B
  12. Find the indicated side: We are looking for b A 50o b = ? 70o Ca = 12B
  13. Find the indicated side: A 50o b = ? 70o Ca = 12B
  14. Find the indicated side: A 50o b = ? 70o Ca = 12B
  15. Find the indicated side: A 50o b = ? 70o Ca = 12B b = 12*sine(70) / sine(50)
  16. Find the indicated side: A 50o b = ? 70o Ca = 12B b = 12*sine(70) / sine(50) b = 14.72
  17. Find the indicated angle: A 80o b = 7 ?o Ca = 12B
  18. Find the indicated angle: we are looking for B A 80o b = 7 ?o Ca = 12B
  19. Find the indicated angle: A 80o b = 7 ?o Ca = 12B
  20. Find the indicated angle: A 80o b = 7 ?o Ca = 12B
  21. Find the indicated angle: A 80o b = 7 ?o Ca = 12B 7*sine(80) / 12 = .574 sin-1(.574) = 35o <B = 35o
  22. Student Practice Complete the following three questions on a separate sheet of paper Use the Law of Sines to find the missing side or angle
  23. #1 a = ?
  24. #1 a = 10.17
  25. #2 b = ?
  26. #2 b = 11.04
  27. #3 C = ?
  28. #3 C = 48.62o
  29. Law of Sines Review 5/17 Solving a triangle means to find all the missing sides and angles. Solve ABC, if <A = 33o, <B = 47o, and b = 14 Solving a triangle
  30. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 1. Draw and label a triangle. (it does not matter if the triangle is not to scale.) Solving a triangle
  31. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 2. Can you label anything else now? Solving a triangle
  32. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 2. Can you label anything else now? Solving a triangle
  33. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 2. Can you label anything else now? Solving a triangle
  34. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 3. What capital and lower case pair do you have? Solving a triangle
  35. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 3. What capital and lower case pair do you have? Solving a triangle
  36. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions Solving a triangle
  37. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions Solving a triangle
  38. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions 14*sin33 = 7.625 Solving a triangle
  39. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions 14*sin33 = 7.625 7.625 / sin47 = 10.43 Solving a triangle
  40. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions 14*sin33 = 7.625 7.625 / sin47 = 10.43 a = 10.43 Solving a triangle
  41. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions Solving a triangle
  42. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions 14*sin100 = 13.787 Solving a triangle
  43. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions 14*sin100 = 13.787 13.787 / sin47 = 18.85 Solving a triangle
  44. Law of Sines Review 5/17 Solve ABC, if <A = 33o, <B = 47o, and b = 14 4. Create your two proportions 14*sin100 = 13.787 13.787 / sin47 = 18.85 c = 18.85 Solving a triangle
  45. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 1. Draw and label a triangle. (it does not matter if the triangle is not to scale.) Solving a triangle
  46. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 2. Can you label anything else now? Solving a triangle
  47. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 2. Can you label anything else now? Can’t label anything else Solving a triangle
  48. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 3. What capital and lower case pair do you have? Solving a triangle
  49. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 3. What capital and lower case pair do you have? Solving a triangle
  50. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions Solving a triangle
  51. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions Solving a triangle
  52. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions 14*sin98 = 13.864 Solving a triangle
  53. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions 14*sin98 = 13.864 13.864 / 20 = 0.693 Solving a triangle
  54. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions 14*sin98 = 13.864 13.864 / 20 = 0.693 sin-1(0.693) = 43.88o Solving a triangle
  55. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions 14*sin98 = 13.864 13.864 / 20 = 0.693 sin-1(0.693) = 43.88o B = 43.88o Solving a triangle
  56. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions Solving a triangle
  57. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions Solving a triangle
  58. Law of Sines Review 5/17 Solve ABC, if <C = 98o, b = 14, c = 20 4. Create your two proportions 20*sin38.12 = 12.346 12.346 / sin98 = 12.47 a = 12.47 Solving a triangle
  59. Law of Sines Steps: 1. Draw and label the triangle 2. Can you label anything else? 3. What capital and lower case pair do you have? 4. Create and solve your two proportions
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