立體測量 (18)
Author: 藍邦偉  老師

x

y

z

單位向量

顯示座標軸

$第%v步$

C

A

B

分解三角形

O_1

H_1

A_1

B_1

O_2

H_2

O_3

C_1

H_3

O

A

B

C

θ

180°-θ

h

h

h

h

h

\sqrt{3}h

\sqrt{3}h

\frac{h}{\sqrt{3}}

\frac{h}{\sqrt{3}}

h

\sqrt{3}h

\frac{h}{\sqrt{3}}

h

x

y

z

$ O $

$ H $

$ P $

$ 立體測量\;(18) $

$ 立體測量\;(18) $

$ O $

$ A $

$ C $

$ B $

$ O_1 $

$ O_2 $

$ O_3 $

$ H_1 $

$ H_2 $

$ H_3 $

$ A_1 $

$ B_1 $

$ C_1 $

$ A $

$ B $

$ C $

$ 在筆直的馬路上相異三點A,\;B,\;C\;測量建築物的高度，\;其仰角分別為30°，\;45°，\;60° ，\;若\overline{AB}=100公尺，\;$
$\overline{AC}=200公尺，\;試求此建築物的高度.$

O = (9.8, 1.3)
β = 1 rad (slider from 1.4486232791552935 to 1.6929693744344996, step 0.017453292519943295)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
j_2 = Ray(O, O + w)
α = 4.71238898038469 rad (slider from 3.6651914291880923 to 5.585053606381854, step 0.017453292519943295)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
u = Vector(O, X_{unit})
v = Vector(O, Y_{unit})
L = 7 (slider from 1 to 10, step 1)
a = Vector(O - L * v, O + L * v)
b = Vector(O - L * w, O + L * w)
z = Vector(O - L * u, O + L * u)
A_1: O + L * u
B_1: O + L * v
Z: O + L * w
c = false
d = false
n = 0 (slider from 0 to 5, step 1)
h = 6.3 (slider from 0 to 8, step 0.01)
H = Point(j_2)
s = Segment(H, O)
x_1: x = x(Corner[1])
x_2: x = x(Corner[2])
P_1: O + 7 * u
m = Line(P_1, v)
P_a = Intersect(x_1, m)
P_b = Intersect(x_2, m)
t = 0 (slider from 0 to 1, step 0.0010)
P: P_b + t * Vector[P_b, P_a]
f = Segment(H, P)
r = Segment(P, O)
P_3: P + (-2.34, -0.05)
P_4: P + (2.37, 0.02)
Tire_F = Circle(P_3, 0.65)
Tire_R = Circle(P_4, 0.65)
H_F = Circle(P_3, 0.2)
H_R = Circle(P_4, 0.2)
γ = 0 rad (slider from 0 to 6.283185307179586, step 1.7453292519943296E-4)
Q_0: P_4 + (0.52 * cos(γ + 288°), 0.52 * sin(γ + 288°))
Q_1: P_3 + (0.52 * cos(γ), 0.52 * sin(γ))
Q_2: P_3 + (0.52 * cos(γ + 72°), 0.52 * sin(γ + 72°))
Q_3: P_3 + (0.52 * cos(γ + 144°), 0.52 * sin(γ + 144°))
Q_4: P_3 + (0.52 * cos(γ + 216°), 0.52 * sin(γ + 216°))
Q_5: P_3 + (0.52 * cos(γ + 288°), 0.52 * sin(γ + 288°))
Q_6: P_4 + (0.52 * cos(γ), 0.52 * sin(γ))
Q_7: P_4 + (0.52 * cos(γ + 72°), 0.52 * sin(γ + 72°))
Q_8: P_4 + (0.52 * cos(γ + 144°), 0.52 * sin(γ + 144°))
Q_9: P_4 + (0.52 * cos(γ + 216°), 0.52 * sin(γ + 216°))
q_0 = Segment(P_4, Q_0)
q_1 = Segment(P_3, Q_1)
q_2 = Segment(P_3, Q_2)
q_3 = Segment(P_3, Q_3)
q_4 = Segment(P_3, Q_4)
q_5 = Segment(P_3, Q_5)
q_6 = Segment(P_4, Q_6)
q_7 = Segment(P_4, Q_7)
q_8 = Segment(P_4, Q_8)
q_9 = Segment(P_4, Q_9)
c_1 = Circle(O, 0.5)
多邊形1, i, j, k, l = Polygon(Corner[1], Corner[2], Corner[3], Corner[4])
S = Intersect(c_1, s)
N = Intersect(c_1, r)
Q: S + N - O
s_1 = Segment(Q, N)
s_2 = Segment(Q, S)
R_3: P_1 + 6 * v
R_1: P_1 - 4 * v
e = Segment(R_1, R_3)
R_2 = Point(e)
g = Segment(O, R_1)
p = Segment(O, R_2)
q = Segment(O, R_3)
a_1 = Segment(H, R_1)
b_1 = Segment(H, R_2)
d_1 = Segment(H, R_3)
A = Intersect(c_1, g, 1)
B = Intersect(c_1, p, 1)
C = Intersect(c_1, q, 1)
S_1: S + C - O
e_1 = Segment(S, S_1)
f_1 = Segment(S_1, C)
D: A + S - O
g_1 = Segment(D, A)
h_1 = Segment(D, S)
E: B + S - O
i_1 = Segment(E, S)
j_1 = Segment(E, B)
m_2 = Segment(R_1, R_2)
文字6: "" + m_2
k_1 = Segment(R_2, R_3)
文字7: "" + k_1
V = (1.6334129243382471, 4.847252246532099)
V_2: V + (0, 3)
V_1: V - (sqrt(3), 0)
W: V + (1.5, 0)
W_1: W + (3, 0)
W_2: W_1 + (0, 3)
F: W_1 + (1.5, 0)
F_1: F + (3 * sqrt(3), 0)
F_2: F + (0, 3)
l_1 = Segment(V_2, V)
m_1 = Segment(V, V_1)
n_1 = Segment(V_1, V_2)
p_1 = Segment(W, W_1)
r_1 = Segment(W_1, W_2)
t_1 = Segment(W_2, W)
a_2 = Segment(F_2, F)
b_2 = Segment(F, F_1)
c_2 = Segment(F_1, F_2)
δ = Angle(V_2, V_1, V)
ε = Angle(W_1, W, W_2)
ζ = Angle(F, F_1, F_2)
G: V + (4, -1.5)
I = (1.4794492125024912, 0.3163201553655642)
d_2: y = y(I)
J = Point(d_2)
K = Point(d_2)
M = Point(d_2)
e_2 = Segment(G, J)
f_2 = Segment(G, K)
g_2 = Segment(G, M)
h_2 = Segment(J, K)
i_2 = Segment(K, M)
η = Angle(V_1, V, V_2)
θ = Angle(W_2, W_1, W)
ι = Angle(F_2, F, F_1)
κ = Angle(G, K, J)
λ = Angle(G, K, M)