立體測量 (14)
Author: 藍邦偉  老師

x

y

z

單位向量

座標軸

$第%v步$

x

y

z

$ 立體測量\;(14) $

$ A $

$ O $

$ C $

$ H $

$ 從相距1000公尺的A,\;B\;兩點，\;觀測飛機H，\;在A測得\overline{AB},\; \overline{AC}\;所成之角為75°，\;飛機的仰角為30°，\;在 B\;$
$測得\overline{BA},\;\overline{BC}\;所成之角為 60°，\;試求飛機的高度. $

$ 地面上A,\;B\;兩點相距20\sqrt{2}公尺，\; 今測得飛機H\;之仰角分別為30°,\;45°，\;且由H測得A,B兩點的視角$
$(即∠AHB)為135°，\;試求飛機的高度.$

$ 已知一飛機高度為20000呎，\;欲測量地面上A,\;B\;兩地的距離，\;今測得A地的俯角為30°，\; B地的俯角$
$為60°，\;且∠AHB=135°，\;試求A,\;B\;兩地的距離.$

α = 3.8746309394274117 rad (slider from 3.7000980142279785 to 4.049163864626845, step 0.0017453292519943296)
β = 1.5184364492350666 rad (slider from 1.4835298641951802 to 1.7453292519943295, step 0.008726646259971648)
O = (13.28866586317749, 3.819494481810299)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
Z_{unit}: O + (0, sin(β))
u = Vector(O, X_{unit})
v = Vector(O, Y_{unit})
w = Vector(O, Z_{unit})
L = 5 (slider from 1 to 10, step 1)
a = Vector(O - L * v, O + L * v)
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
e = Ray(O, A_1)
A = Point(e)
n = 0 (slider from 0 to 6, step 1)
f = Segment(O, A)
F: O + 25 * u + 32.6 * v
t = 0 (slider from 0 to 22, step 0.0010)
C: F + t * u
B = (15.534136621509363, 1.1081335305208808)
g: x = x(C)
H = Point(g)
h = Segment(H, C)
i = Segment(A, C)
j = Segment(C, O)
k = Segment(O, H)
l = Segment(H, A)
p = Circle(C, 0.5)
E = Intersect(p, i)
G = Intersect(p, h)
H_1 = Intersect(p, j)
I: G + E - C
m = Segment(I, G)
q = Segment(I, E)
J: G + H_1 - C
r = Segment(J, G)
s = Segment(J, H_1)
b = Vector(O, O + L * w)
多邊形1, a_1, b_1, c_1, d_1 = Polygon(Corner[1], Corner[2], Corner[3], Corner[4])