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Find Angles Using Trigonometry

Find Angles Using Trigonometry
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2017-06-20 07:09
AngleTrigonometry
This example demonstrates how to find angles using trigonometry. It covers core math concepts such as trigonometric functions and angle calculations. GeoGebra commands used include Random, Line, OrthogonalLine, Segment, Intersect, Polygon, Angle, Midpoint, Length, If, etc. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Random(1, 4) → randn
  2. Line(A, B) → f
  3. OrthogonalLine(C, f) → g
  4. Segment(C, B) → h
  5. Intersect(f, g) → D
  6. Polygon(C, D, B) → poly1, b, c, d
  7. Angle(D, C, B) → α
  8. Angle(C, B, D) → β
  9. Angle(B, D, C) → γ
  10. Random(1, 6) → questionrand
  11. Midpoint(C, B) → E
  12. Midpoint(B, D) → F
  13. Midpoint(D, C) → G
  14. Length(Segment[C, D]) → Segb
  15. Length(Segment[D, B]) → Segc
  16. Length(Segment[B, C]) → Segd
  17. Line(A_1, B_1) → f_1
  18. OrthogonalLine(C_1, f_1) → g_1
  19. Segment(C_1, B_1) → h_1
  20. Intersect(f_1, g_1) → D_1
  21. Polygon(C_1, D_1, B_1) → poly1_1, b_1, c_1, d_1
  22. Angle(D_1, C_1, B_1) → α_1
  23. Angle(C_1, B_1, D_1) → β_1
  24. Angle(B_1, D_1, C_1) → γ_1
  25. Midpoint(C_1, B_1) → E_1
  26. Midpoint(B_1, D_1) → F_1
  27. Midpoint(D_1, C_1) → G_1
  28. Line(A_2, B_2) → f_2
  29. OrthogonalLine(C_2, f_2) → g_2
  30. Segment(C_2, B_2) → h_2
  31. Intersect(f_2, g_2) → D_2
  32. Polygon(C_2, D_2, B_2) → poly1_2, b_2, c_2, d_2
  33. Angle(D_2, C_2, B_2) → α_2
  34. Angle(C_2, B_2, D_2) → β_2
  35. Angle(B_2, D_2, C_2) → γ_2
  36. Midpoint(C_2, B_2) → E_2
  37. Midpoint(B_2, D_2) → F_2
  38. Midpoint(D_2, C_2) → G_2
  39. If(j ≟ 1 ∨ j ≟ 2, "CAH", If[j ≟ 3 ∨ j ≟ 4, "SOH", If[j ≟ 5 ∨ j ≟ 6, "TOA", "ANSWERS"]]) → captionSlider
  40. Line(A_5, B_5) → f_5
  41. OrthogonalLine(C_5, f_5) → g_5
  42. Segment(C_5, B_5) → h_3
  43. Intersect(f_5, g_5) → D_5
  44. Polygon(C_5, D_5, B_5) → poly1_4, b_4, c_4, d_4
  45. Angle(D_5, C_5, B_5) → α_3
  46. Angle(C_5, B_5, D_5) → β_4
  47. Angle(B_5, D_5, C_5) → γ_3
  48. Midpoint(C_5, B_5) → E_3
  49. Midpoint(B_5, D_5) → F_3
  50. Midpoint(D_5, C_5) → G_3
  51. Line(A_4, B_4) → f_4
  52. OrthogonalLine(C_4, f_4) → g_4
  53. Segment(C_4, B_4) → h_4
  54. Intersect(f_4, g_4) → D_4
  55. Polygon(C_4, D_4, B_4) → poly1_5, b_5, c_5, d_5
  56. Angle(D_4, C_4, B_4) → α_4
  57. Angle(C_4, B_4, D_4) → β_3
  58. Angle(B_4, D_4, C_4) → γ_4
  59. Midpoint(C_4, B_4) → E_4
  60. Midpoint(B_4, D_4) → F_4
  61. Midpoint(D_4, C_4) → G_4
  62. Line(A_8, B_8) → f_8
  63. OrthogonalLine(C_8, f_8) → g_8
  64. Segment(C_8, B_8) → h_6
  65. Intersect(f_8, g_8) → D_8
  66. Polygon(C_8, D_8, B_8) → poly1_7, b_7, c_7, d_7
  67. Angle(D_8, C_8, B_8) → α_6
  68. Angle(C_8, B_8, D_8) → β_7
  69. Angle(B_8, D_8, C_8) → γ_6
  70. Midpoint(C_8, B_8) → E_6
  71. Midpoint(B_8, D_8) → F_6
  72. Midpoint(D_8, C_8) → G_6
  73. Line(A_7, B_7) → f_7
  74. OrthogonalLine(C_7, f_7) → g_7
  75. Segment(C_7, B_7) → h_7
  76. Intersect(f_7, g_7) → D_7
  77. Polygon(C_7, D_7, B_7) → poly1_8, b_8, c_8, d_8
  78. Angle(D_7, C_7, B_7) → α_7
  79. Angle(C_7, B_7, D_7) → β_6
  80. Angle(B_7, D_7, C_7) → γ_7
  81. Midpoint(C_7, B_7) → E_7
  82. Midpoint(B_7, D_7) → F_7
  83. Midpoint(D_7, C_7) → G_7
  84. Line(A_{11}, B_{11}) → f_{11}
  85. OrthogonalLine(C_{11}, f_{11}) → g_{11}
  86. Segment(C_{11}, B_{11}) → h_9
  87. Intersect(f_{11}, g_{11}) → D_{11}
  88. Polygon(C_{11}, D_{11}, B_{11}) → poly1_{10}, b_{10}, c_{10}, d_{10}
  89. Angle(D_{11}, C_{11}, B_{11}) → α_9
  90. Angle(C_{11}, B_{11}, D_{11}) → β_{10}
  91. Angle(B_{11}, D_{11}, C_{11}) → γ_9
  92. Midpoint(C_{11}, B_{11}) → E_9
  93. Midpoint(B_{11}, D_{11}) → F_9
  94. Midpoint(D_{11}, C_{11}) → G_9
  95. Line(A_{10}, B_{10}) → f_{10}
  96. OrthogonalLine(C_{10}, f_{10}) → g_{10}
  97. Segment(C_{10}, B_{10}) → h_{10}
  98. Intersect(f_{10}, g_{10}) → D_{10}
  99. Polygon(C_{10}, D_{10}, B_{10}) → poly1_{11}, b_{11}, c_{11}, d_{11}
  100. Angle(D_{10}, C_{10}, B_{10}) → α_{10}
  101. Angle(C_{10}, B_{10}, D_{10}) → β_9
  102. Angle(B_{10}, D_{10}, C_{10}) → γ_{10}
  103. Midpoint(C_{10}, B_{10}) → E_{10}
  104. Midpoint(B_{10}, D_{10}) → F_{10}
  105. Midpoint(D_{10}, C_{10}) → G_{10}