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仰角与俯角 by Ooi Soo Huat

仰角与俯角 by Ooi Soo Huat
几何画板及绘图内容加载中，请稍等……
2017-11-28 21:18
角向量三角函数
所属专题 Mathematics Form 1
本范例演示仰角与俯角的概念及其应用。涉及的核心数学概念包括角度、向量和三角函数。通过使用GeoGebra命令如SelectedIndex、Line、Angle等，可以构造出动态的几何图形，帮助学生理解角度在实际问题中的应用。适合高中数学教学和学习。

GeoGebra 命令及参数

  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