Law of Sines: Intro via Areas

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A
2. Circle(A, 1) → c
3. Rotate((1, 0), (a * π / 180), A) → B
4. Rotate(D, (a * π / 180), C) → D'
5. Ray(C, D') → f
6. Segment(C, D) → g
7. Rotate(C, ((-b) * π / 180), D) → C'
8. Ray(D, C') → h
9. Intersect(f, h) → E
10. Segment(C, E) → i
11. Segment(E, D) → j
12. Rotate((-1, 0), ((-b) * π / 180), A) → F
13. Segment(A, B) → k
14. Segment(A, F) → l
15. Min({1, i, g, j}) → d
16. Circle(C, (0.45 * d)) → e
17. Circle(E, (0.45 * d)) → p
18. Circle(D, (0.45 * d)) → q
19. Intersect(e, g, 1) → G
20. Intersect(e, i, 1) → H
21. Intersect(p, j, 1) → I
22. Intersect(p, i, 1) → J
23. Intersect(q, g, 1) → K
24. Intersect(q, j) → L,
25. CircleSector(C, G, H) → r
26. CircleSector(D, L, K) → t
27. Line(C, xAxis) → m
28. Point(m) → M
29. Angle(M, C, G) → α
30. Dilate(C, If[0 < n ≤ 1, 1 - n, 0], A) → C'_{1}
31. Vector(C, C'_{1}) → u
32. Translate(r, u) → r'
33. Rotate(r', If[0 < n ≤ 1, ((-n) * α), (-α)], C'_{1}) → r''
34. Line(D, xAxis) → f_1
35. Point(f_1) → N
36. Angle(N, D, K) → β
37. Dilate(D, If[1 < n ≤ 2, 2 - n, 0], A) → D'_{1}
38. Vector(D, D'_{1}) → v
39. Translate(t, v) → t'
40. Rotate(t', If[1 < n ≤ 2, ((-β) * (n - 1)), (-β)], D'_{1}) → t''
41. Dilate(B, If[2 < n ≤ 3, 3 - n, 0], O) → B'
42. Dilate(F, If[2 < n ≤ 3, 3 - n, 0], P) → F'
43. Segment(B, B') → g_1
44. Segment(F, F') → h_1
45. Angle(B, O, A) → γ
46. Angle(A, P, F) → δ
47. Dilate(B, If[4 < n ≤ 5, 5 - n, 0], E) → B'_{1}
48. Vector(B, B'_{1}) → u_1
49. Translate(B, u_1) → B'_{2}
50. Translate(B', u_1) → B''
51. Segment(B'_{2}, B'') → i_1
52. OrthogonalLine(E, i) → j_1
53. Line(E, g_1) → k_1
54. Point(j_1) → Q
55. Point(k_1) → R
56. Angle(Q, E, R) → ε
57. Rotate(B'_{2}, If[4 < n ≤ 5, ((-(n - 4)) * ε), (-ε)], B'_{2}) → S
58. Rotate(B'', If[4 < n ≤ 5, ((-(n - 4)) * ε), (-ε)], B'_{2}) → B'''
59. Segment(S, B''') → l_1
60. Angle(Q, E, C) → ζ
61. Dilate(E, If[5 < n ≤ 6, 6 - n, 0], B''') → E'
62. Vector(E, E') → v_1
63. Translate(C, v_1) → C'_{2}
64. Translate(E, v_1) → E'_{1}
65. Segment(C'_{2}, E'_{1}) → i'
66. Angle(E, C, C'_{2}) → η
67. Dilate(E, If[6 < n ≤ 7, 7 - n, 0], C) → E'_{2}
68. Vector(E, E'_{2}) → w_1
69. Translate(S, w_1) → S'
70. Translate(B''', w_1) → T
71. Segment(S', T) → m_1
72. Dilate(P, If[8 < n ≤ 9, 9 - n, 0], D) → P'
73. Vector(P, P') → a_1
74. Translate(F, a_1) → F'_{1}
75. Translate(F', a_1) → F''
76. Segment(F'_{1}, F'') → n_1
77. OrthogonalLine(D, j) → p_1
78. Line(D, h_1) → q_1
79. Point(q_1) → U
80. Point(p_1) → V
81. Angle(U, D, V) → θ
82. Rotate(F'_{1}, If[8 < n ≤ 9, ((n - 8) * θ), θ], F'') → W
83. Rotate(F'', If[8 < n ≤ 9, ((n - 8) * θ), θ], F'') → F'''
84. Segment(W, F''') → r_1
85. Angle(W, D, E) → ι
86. Dilate(D, If[9 < n ≤ 10, 10 - n, 0], E) → D'_{2}
87. Vector(D, D'_{2}) → b_1
88. Translate(W, b_1) → W'
89. Translate(F''', b_1) → Z
90. Segment(W', Z) → s_1
91. Angle(D, E, W') → κ
92. Dilate(E, If[10 < n ≤ 11, 11 - n, 0], W') → E'_{3}
93. Vector(E, E'_{3}) → c_1
94. Translate(E, c_1) → E'_{4}
95. Translate(D, c_1) → D'_{3}
96. Segment(E'_{4}, D'_{3}) → j'
97. Polygon(D, W, W', E) → q1, d_1, w_2, w', e_1
98. Circle(D, i) → t_1
99. Ray(W, W') → f_2
100. Intersect(t_1, f_2) → A_1,
101. Dilate(W, If[13 < n ≤ 14, 14 - n, 0], A_1) → W'_{1}
102. Vector(W, W'_{1}) → u_2
103. Translate(W', u_2) → W''
104. Polygon(D, W'_{1}, W'', E) → q2, d_2, w'_{1}, w'', e_2
105. Line(A_1, D) → g_2
106. Line(W'', E) → i_2
107. OrthogonalLine(D, g_2) → h_2
108. Intersect(i_2, h_2) → B_1
109. Dilate(E, If[15 < n ≤ 16, 16 - n, 0], B_1) → E'_{5}
110. Vector(E, E'_{5}) → v_2
111. Translate(W'', v_2) → W'''
112. Polygon(D, W'_{1}, W''', E'_{5}) → q3, d_3, j_2, w''', e'_{5}
113. Dilate(W''', If[17 < n ≤ 18, 18 - n, 0], B''') → C_1
114. Vector(W''', C_1) → a_2
115. Translate(D, a_2) → D'_{4}
116. Translate(W'_{1}, a_2) → D_1
117. Translate(W''', a_2) → E_1
118. Translate(E'_{5}, a_2) → F_1
119. Polygon(D'_{4}, D_1, E_1, F_1) → q3', d'_{4}, k_2, l_2, m_2
120. Line(B''', g_2) → n_2
121. Point(n_2) → G_1
122. Angle(C'_{2}, B''', G_1) → λ
123. Rotate(D'_{4}, If[17 < n ≤ 18, ((-(n - 17)) * λ), (-λ)], E_1) → H_1
124. Rotate(D_1, If[17 < n ≤ 18, ((-(n - 17)) * λ), (-λ)], E_1) → I_1
125. Rotate(E_1, If[17 < n ≤ 18, ((-(n - 17)) * λ), (-λ)], E_1) → J_1
126. Rotate(F_1, If[17 < n ≤ 18, ((-(n - 17)) * λ), (-λ)], E_1) → K_1
127. Polygon(H_1, I_1, J_1, K_1) → q3'', p_2, q_2, r_2, s_2
128. Line(W', W) → t_2
129. Line(E, D) → b_2
130. Line(W'_{1}, D) → c_2
131. Line(W''', E) → f_3
132. Segment((-1, 0), (1, 0)) → s
133. Point(c) → L_1
134. Segment((0, 0), L_1) → g_3