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Angle of Elevation and Depression

Angle of Elevation and Depression
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2017-11-28 21:18
AngleVectorTrigonometry
In collections Mathematics Form 1
This example demonstrates the concepts of angle of elevation and depression and their applications. Key mathematical concepts include angles, vectors, and trigonometry. Using GeoGebra commands such as SelectedIndex, Line, Angle, etc., dynamic geometric figures are constructed to help students understand the application of angles in real-world problems. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. SelectedIndex(Bahasa) → nn
  2. Line(A, xAxis) → a
  3. Line(B, xAxis) → b
  4. OrthogonalLine(A, b) → c
  5. Intersect(b, c) → C
  6. OrthogonalLine(B, a) → f
  7. Intersect(a, f) → D
  8. Vector(B, C) → u
  9. Vector(B, A) → v
  10. Angle(u, v) → D_1
  11. Vector(A, D) → w
  12. Angle(w, Vector[(-v)]) → T_1
  13. Segment(A, B) → d
  14. Rotate(A, (Ar * D_1), B) → A'
  15. Rotate(B, (Ar * T_1), A) → B'
  16. If(Ar > 0, Rotate[A', (-α), B], Rotate[A', α, B]) → A_1
  17. If(Ar > 0, Rotate[B', (-β), A], Rotate[B', β, A]) → B_1
  18. Vector(B, A_1) → e
  19. Vector(A, B_1) → g
  20. Angle(u, e) → D_2
  21. Angle(w, g) → T_2
  22. Circle(A, 4) → h
  23. Intersect(h, a, 1) → E
  24. Intersect(h, a, 2) → F
  25. Circle(B, 4) → k
  26. Intersect(k, b, 1) → G
  27. Intersect(k, b, 2) → H
  28. If(Ar > 0, Rotate[A', (-0.5 * α), B], Rotate[A', (0.5 * α), B]) → A_2
  29. Segment(B, A_2) → i
  30. Circle(B, 2) → p_1
  31. Intersect(p_1, i, 1) → I
  32. If(Ar > 0, Rotate[B', (-0.5 * β), A], Rotate[B', (0.5 * β), A]) → B_2
  33. Segment(A, B_2) → j
  34. Circle(A, 2) → q
  35. Intersect(q, j, 1) → J
  36. Circle(B, 0.75) → r
  37. Segment(B, A_1) → l
  38. Segment(A, B_1) → m
  39. Intersect(r, l, 1) → K
  40. Circle(A, 0.75) → s
  41. Intersect(s, m, 1) → L
  42. Rotate(K, -30°, B) → Be_1
  43. Rotate(K, 30°, B) → Be_2
  44. Midpoint(B, Be_1) → M
  45. Midpoint(B, Be_2) → N
  46. CircleArc(B, M, N) → c_1
  47. Segment(B, Be_1) → n
  48. Segment(B, Be_2) → t
  49. Rotate(L, 30°, A) → L'
  50. Rotate(L, (-(30°)), A) → L'_1
  51. Midpoint(A, L') → O
  52. Midpoint(A, L'_1) → P
  53. CircleArc(A, P, O) → d_1
  54. Segment(A, L') → a_1
  55. Segment(A, L'_1) → b_1
  56. Line(A, B) → e_1
  57. Circle(A, 0.5) → f_1
  58. Intersect(f_1, e_1, 1) → Q
  59. Circle(B, 0.5) → g_1
  60. Intersect(g_1, e_1, 2) → R
  61. Angle(B, C, A) → γ
  62. Angle(A, D, B) → δ
  63. Segment(B, D) → h_1
  64. Segment(A, C) → i_1
  65. Angle(B, C, A) → ε
  66. Segment(A, C) → j_1
  67. Angle(B, D, A) → ζ
  68. Segment(B, D) → k_1
  69. If(ATop ≟ true, "B from A", "A from B") → Tunduk
  70. If(nn ≟ 1, If[ATop ≟ true, "A from B", "B from A"], nn ≟ 2, If[ATop ≟ true, "A dari B", "B dari A"]) → Dongak
  71. If(nn ≟ 1, "Angle of elevation of " + Dongak, "Sudut dongak " + Dongak) → JDongak
  72. If(nn ≟ 1, "Angle of depression of " + Tunduk, "Sudut tunduk " + Tunduk) → JTunduk
  73. If(o ≟ true, JDongak, JTunduk) → DJawap
  74. If(nn ≟ 1, "Horizontal line", "Garis mengufuk") → text1
  75. If(nn ≟ 1, "Horizontal line", "Garis mengufuk") → text2
  76. If(nn ≟ 1, "Horizontal line", "Garis mengufuk") → text3
  77. If(nn ≟ 1, "Horizontal line", "Garis mengufuk") → text4