MathPlotAI Logo MathPlotAI

Sextant

Sextant
Loading the math board and drawing, please wait…
2014-02-18 01:19
AngleTrigonometryCoordinate Geometry
Adjust the sextant to align the image of the sun with the horizon. This example demonstrates the relationship between the angle of elevation and the horizon, involving trigonometry and angles. It uses commands such as Intersect, Circle, Rotate, Angle, CircleArc, Segment, Line, Midpoint, Vector, etc. Suitable for middle school and above students to learn trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, R) → sextantCircle
  3. Point(sextantCircle) → zeroDegrees
  4. Rotate(zeroDegrees, 30*°, O) → zeroDegrees'_1
  5. Angle(zeroDegrees, O, zeroDegrees'_1) → thirtyDegrees2
  6. Rotate(zeroDegrees, 330*°, O) → zeroDegrees'
  7. Angle(zeroDegrees', O, zeroDegrees) → thirtyDegrees1
  8. CircleArc(O, zeroDegrees', zeroDegrees'_1) → sixtantArc
  9. Segment(O, zeroDegrees') → sixtantSegment1
  10. Point(sixtantArc) → A
  11. Segment(O, A) → sixtantSegment2
  12. Point(sixtantArc) → MovablePoint
  13. Point(sixtantSegment1) → mirrorBase
  14. Circle(mirrorBase, r) → c
  15. Line(mirrorBase, yAxis) → verticalMirrorLine
  16. Intersect(c, verticalMirrorLine, 2) → verticalIntersectPoint
  17. Rotate(verticalIntersectPoint, mirrorAngle, mirrorBase) → verticalIntersectPoint'
  18. Angle(verticalIntersectPoint, mirrorBase, verticalIntersectPoint') → mAngle
  19. Circle(O, r / 2) → d
  20. Segment(mirrorBase, verticalIntersectPoint') → mirror1
  21. Midpoint(mirrorBase, verticalIntersectPoint') → mirrorCentre
  22. Line(mirrorCentre, xAxis) → horizonLine
  23. Segment(O, mirrorCentre) → b
  24. Midpoint(O, mirrorCentre) → B
  25. Vector(O, B) → u
  26. OrthogonalLine(mirrorCentre, mirror1) → mirrorNormal
  27. Intersect(c, mirrorNormal, 1) → C
  28. Angle(C, mirrorCentre, O) → angleToNormal
  29. Angle(MovablePoint, O, zeroDegrees'_1) → angleMovable
  30. Point(d) → D
  31. Rotate(D, mirrorAngle - angleMovable, O) → M1
  32. Angle(D, O, M1) → α
  33. Line(M1, O) → e
  34. Intersect(d, e, 2) → M2
  35. Segment(M2, M1) → mirror2
  36. OrthogonalLine(O, mirror2) → mirror2Normal
  37. Intersect(d, mirror2Normal, 2) → E
  38. Angle(E, O, mirrorCentre) → β
  39. Rotate(E, (-β), O) → E'
  40. Angle(E', O, E) → γ
  41. Ray(O, E') → f
  42. Segment(O, MovablePoint) → g
  43. Intersect(d, g, 1) → F
  44. Segment(F, MovablePoint) → h
  45. Point(horizonLine) → HorizonPoint
  46. Line(HorizonPoint, yAxis) → a
  47. Ray(G, H) → i
  48. Point(i) → SunPoint
  49. Point(f) → I
  50. Point(f) → J
  51. Vector(I, J) → v
  52. Point(horizonLine) → K
  53. Circle(SunPoint, r) → k
  54. Segment(SunPoint, O) → j
  55. Intersect(k, j, 1) → L
  56. Mirror(HorizonPoint, yAxis) → HorizonPoint'
  57. Line(HorizonPoint', yAxis) → m
  58. Point(horizonLine) → N
  59. Vector(mirrorCentre, N) → z
  60. Point(horizonLine) → P
  61. Intersect(f, i) → Q
  62. Vector(SunPoint, Q) → p
  63. Translate(HorizonPoint', Vector[(-p)]) → HorizonPoint''
  64. Vector(HorizonPoint', HorizonPoint'') → q
  65. Point(horizonLine) → S
  66. Point(horizonLine) → T
  67. Point(horizonLine) → U
  68. Point(horizonLine) → V
  69. Vector(U, P) → n
  70. Point(horizonLine) → M
  71. Vector(M, K) → w
  72. Segment(K, S) → l
  73. Segment(N, T) → s
  74. Segment(P, V) → t
  75. Rotate(zeroDegrees'_1, 350*°, O) → W
  76. Angle(W, O, zeroDegrees'_1) → δ
  77. Rotate(W, 350*°, O) → W'
  78. Angle(W', O, W) → ε
  79. Rotate(W', 350*°, O) → W''
  80. Angle(W'', O, W') → ζ
  81. Rotate(W'', 350*°, O) → W'''
  82. Angle(W''', O, W'') → η
  83. Rotate(W''', 350*°, O) → Z
  84. Angle(Z, O, W''') → θ
  85. Segment(W, O) → a_1
  86. Segment(W', O) → b_1
  87. Segment(W'', O) → c_1
  88. Segment(W''', O) → d_1
  89. Segment(Z, O) → e_1
  90. Point(xAxis) → A_1
  91. Angle(SunPoint, O, A_1) → ι
  92. Circle(MovablePoint, 1.5) → f_1
  93. Line(O, MovablePoint) → g_1
  94. Intersect(f_1, g_1, 2) → textPoint