三角測量(1)
Author: 藍邦偉  老師

$ 三角測量(1) $

$ h $

$ y $

$ H $

$ A $

$ B $

$ C $

$ O $

O = (10.942, -2.554)
H = Point(x = x(O))
C_2: O + (1, 0)
D: C_2 + H - O
r = Ray(D, R)
A = Point(Ray[C_2, O])
B = Point(Segment[A, O])
a_1 = Segment(O, A)
a_2 = Segment(A, H)
a_3 = Segment(B, H)
a_4 = Segment(O, H)
a_5 = Segment(D, C_2)
α = Angle(O, A, H)
β = Angle(O, B, H)
t_x: "$ x =" + (LaTeX[Distance[A, B]]) + "$"
r_1 = Ray(C_2, C_2 + (1, 0))
C = Point(r_1)
t_{Main}: "$ \left\lbrace\begin{array}{ll} \frac{y}{h} =\frac{1}{tan" + (LaTeX[β]) + "}\\  \frac{x+y}{h}=\frac{1}{tan" + (LaTeX[α]) + "} \\ \end{array}   \right.\  $
$⇒\frac{x}{h}=\frac{1}{tan" + (LaTeX[α]) + "} -\frac{1}{tan" + (LaTeX[β]) + "}$
$\;\;\;\;\;\;\;\;=\frac{tan" + (LaTeX[β]) + "-tan" + (LaTeX[α]) + "}{tan" + (LaTeX[β]) + " tan" + (LaTeX[α]) + "}$
$⇒h=\frac{tan" + (LaTeX[α]) + " tan" + (LaTeX[β]) + "}{tan" + (LaTeX[β]) + " -tan" + (LaTeX[α]) + "}\;x$
$\;\;\;\;\;\;\;\;=\frac{" + (LaTeX[tan(α) * tan(β)]) + "}{" + (LaTeX[tan(β)]) + "-" + (LaTeX[tan(α)]) + "}\;x$
$\;\;\;\;\;\;\;\;=" + (LaTeX[tan(α) * tan(β) / (tan(β) - tan(α))]) + "\;x$
$\;\;\;\;\;\;\;\;=" + (LaTeX[tan(α) * tan(β) / (tan(β) - tan(α)) * Distance[A, B]]) + "$"