三角形面積公式
Author: 藍邦偉　老師
Date: 7 1 月 2013

$A$

$B$

$C$

$ 三角形面積公式 $

$ \Delta ABC=\frac{1}{2}\;ab\;sinC=\frac{1}{2}\; bc\;sinA=\frac{1}{2}\;ca\;sinB$

A = (3.941037567084078, -1.871699463327366)
B = (7.126511627906976, 5.284400715563505)
C = (12.016887298747763, 0.07996422182468979)
多邊形1, c, a, b = Polygon(A, B, C)
d = Circle(A, B, C)
s = 0 (slider from 0 to 3, step 1)
α = Angle(B, A, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
r = Radius(d)
h_1 = OrthogonalLine(A, a)
D = Intersect(h_1, a)
h = OrthogonalLine(B, b)
E = Intersect(h, b)
i = OrthogonalLine(C, c)
F = Intersect(i, c)
h_2 = Segment(A, D)
h_4 = Segment(F, C)
a_1 = Line(B, C)
f = Line(C, A)
j = Line(A, B)
h_3 = OrthogonalLine(A, a_1)
l = OrthogonalLine(B, f)
m = OrthogonalLine(C, j)
G = Intersect(a_1, h_3)
H = Intersect(f, l)
I = Intersect(j, m)
h_a = Segment(A, G)
h_b = Segment(B, H)
h_c = Segment(C, I)
δ = Angle(C, I, B)
ε = Angle(B, H, C)
ζ = Angle(C, G, A)
text1: "$ \Delta=\frac{1}{2}\;a\cdot h_a=\frac{1}{2}absinC $
$\;\;\;\;=\frac{1}{2}\times" + (LaTeX[a]) + "\times" + (LaTeX[b]) + "sin" + (LaTeX[γ]) + "$
$\;\;\;\;=" + (LaTeX[0.5 * a * b]) + "\times" + (LaTeX[sin(γ)]) + "$
$\;\;\;\;=" + (LaTeX[a * b * sin(γ) / 2]) + "$"
text2: "$ \Delta=\frac{1}{2}\;b\cdot h_b=\frac{1}{2}bcsinA $
$\;\;\;\;=\frac{1}{2}\times" + (LaTeX[b]) + " \times" + (LaTeX[c]) + " sin" + (LaTeX[α]) + "$
$\;\;\;\;=" + (LaTeX[b * c / 2]) + " \times " + (LaTeX[sin(α)]) + "$
$\;\;\;\;= " + (LaTeX[b * c * sin(α) / 2]) + "$"
text3: "$ \Delta=\frac{1}{2}\;c\cdot h_c=\frac{1}{2}casinB $
$\;\;\;\;=\frac{1}{2}\times" + (LaTeX[c]) + " \times " + (LaTeX[a]) + "sin" + (LaTeX[β]) + " $
$\;\;\;\;=" + (LaTeX[a * c / 2]) + " \times" + (LaTeX[sin(β)]) + " $
$\;\;\;\;= " + (LaTeX[a * c * sin(β) / 2]) + "$"
Q: Corner[4] + (0.2, -1)
text4: "$ a=" + (LaTeX[a]) + " $"
text5: "$b= " + (LaTeX[b]) + " $"
text6: "$c= " + (LaTeX[c]) + " $"