三角測量 (24)
Author: 藍邦偉  老師

湖中有一小島，已知高度為a，測量對岸高峰的仰角為α，高峰在水面倒影的俯角為β。求對岸高峰的高度。

三角測量 (24)

t = 0.9 (slider from 0 to 2, step 0.01)
B = (5.3, 4.44)
B_1 = (8.44, 0.66)
A_1 = (-2.36, 1.22)
a: y = y(A_1)
A = Point(a)
E_1: A + t * (0.2, 1.0)
F: A + (1.0, 0.0)
F_1: (x(F) - 0.2 * t, y(E_1))
d = Ray(E_1, F_1)
C = Mirror(B, a)
j = Segment(B, C)
b = OrthogonalLine(B, a)
D_3 = Intersect(a, b)
D_1: D_3 + (0.5, 0.0)
D_2: D_3 - (0.5, 0.0)
多邊形1, d_1, c, d_2 = Polygon(B, D_2, D_1)
多邊形2, d_3, d_4, c' = Polygon(D_2, C, D_1)
多邊形3, e, f, f_1, e_1 = Polygon(A, F, F_1, E_1)
g = Segment(F_1, B)
h = Segment(F_1, C)
D = Intersect(d, j)
i = Segment(F_1, D)
α = Angle(D, F_1, B)
β = Angle(C, F_1, D)

Tool: wheel
Input: A, α, R, r, r_1
Output: 多邊形1, 多邊形3, 多邊形2, 多邊形4, 多邊形5, d, c, e, p_0, p_1, p_3, p_4, p_2, p_6, p_5, p_8, p_7, q_0, q_1, q_2, q_3, q_5, q_6, q_4, p_9, q_7, q_8, q_9

c = Circle(A, R)
d = Circle(A, r)
P_0: A + (r * cos(α + 298.0°), r * sin(α + 298.0°))
P_1: A + (r * cos(α - 10.0°), r * sin(α - 10.0°))
P_2: A + (r * cos(α + 10.0°), r * sin(α + 10.0°))
P_3: A + (r * cos(α + 62.0°), r * sin(α + 62.0°))
P_4: A + (r * cos(α + 82.0°), r * sin(α + 82.0°))
P_5: A + (r * cos(α + 134.0°), r * sin(α + 134.0°))
P_6: A + (r * cos(α + 154.0°), r * sin(α + 154.0°))
P_7: A + (r * cos(α + 206.0°), r * sin(α + 206.0°))
P_8: A + (r * cos(α + 226.0°), r * sin(α + 226.0°))
P_9: A + (r * cos(α + 278.0°), r * sin(α + 278.0°))
e = Circle(A, r_1)
Q_1: A + (r_1 * cos(α - 15.0°), r_1 * sin(α - 15.0°))
Q_2: A + (r_1 * cos(α + 15.0°), r_1 * sin(α + 15.0°))
Q_3: A + (r_1 * cos(α + 57.0°), r_1 * sin(α + 57.0°))
Q_4: A + (r_1 * cos(α + 87.0°), r_1 * sin(α + 87.0°))
Q_5: A + (r_1 * cos(α + 129.0°), r_1 * sin(α + 129.0°))
Q_6: A + (r_1 * cos(α + 159.0°), r_1 * sin(α + 159.0°))
Q_7: A + (r_1 * cos(α + 201.0°), r_1 * sin(α + 201.0°))
Q_8: A + (r_1 * cos(α + 231.0°), r_1 * sin(α + 231.0°))
Q_9: A + (r_1 * cos(α + 273.0°), r_1 * sin(α + 273.0°))
Q_0: A + (r_1 * cos(α + 303.0°), r_1 * sin(α + 303.0°))
多邊形1_1, p_{17}, p_{10}, q_{17}, q_{10} = Polygon(P_1, P_2, Q_2, Q_1)
多邊形1, p_1, p_2, q_2, q_1 = Polygon(P_1, P_2, Q_2, Q_1)
多邊形2_1, p_{13}, p_{14}, q_{14}, q_{13} = Polygon(P_3, P_4, Q_4, Q_3)
多邊形2, p_3, p_4, q_4, q_3 = Polygon(P_3, P_4, Q_4, Q_3)
多邊形3_1, p_{11}, p_{12}, q_{11}, q_{12} = Polygon(P_5, P_6, Q_6, Q_5)
多邊形3, p_5, p_6, q_6, q_5 = Polygon(P_5, P_6, Q_6, Q_5)
多邊形4_1, p_{15}, p_{16}, q_{15}, q_{16} = Polygon(P_7, P_8, Q_8, Q_7)
多邊形4, p_7, p_8, q_8, q_7 = Polygon(P_7, P_8, Q_8, Q_7)
多邊形5_1, p_{18}, p_{19}, q_{18}, q_{19} = Polygon(P_9, P_0, Q_0, Q_9)
多邊形5, p_9, p_0, q_0, q_9 = Polygon(P_9, P_0, Q_0, Q_9)