正弦定理

三角形の3つの辺の長さ、３つの内角のサインを
具体的に計算してみて、
正弦定理がいつでも成り立っているかを確認しよう。

原点(中心)

円の半径

点C

点B

点A

角度CBA

線分AB

線分BC

線分CA

角度BAC

角度ACB

$ \frac{AB}{\sin(∠BCA)} = \frac{BC}{\sin(∠CAB)} = \frac{CA}{\sin(∠ABC)} = 2R $

三角形の頂点・円の半径を
変えて、計算結果を観察しよう。

O = Intersect(xAxis, yAxis)
X = Point(yAxis)
r = Segment(O, X)
g: (2 * r)
外接円 = Circle(O, X)
C = Point(外接円)
B = Point(外接円)
A = Point(外接円)
β = Angle(C, B, A)
f: Distance[A, C] / sin(β)
b: sin(β)
三角形, AB, BC, CA = Polygon(A, B, C)
α = Angle(B, A, C)
e: Distance[B, C] / sin(α)
a: sin(α)
γ = Angle(A, C, B)
d: Distance[A, B] / sin(γ)
c: sin(γ)
sinβの数値: "" + b + ""
半径表示: "R=" + r + ""
text1: "sin∠ABC = sin( " + β + " ) = " + sinβの数値 + ""
text2: "sin∠BCA = sin( " + γ + " ) = " + c + ""
text3: "sin∠CAB = sin( " + α + " ) = " + a + ""
text_1: "$ \frac{" + (LaTeX[AB]) + "}{" + (LaTeX[c]) + "}  =" + (LaTeX[d]) + "$"
text_2: "$ \frac{" + (LaTeX[BC]) + "}{" + (LaTeX[a]) + "} = " + (LaTeX[e]) + " $"
text_3: "$ \frac{" + (LaTeX[CA]) + "}{" + (LaTeX[b]) + "} = " + (LaTeX[f]) + " $"
text_4: "2R = 2×" + r + " = " + g + ""
テキスト3: "  " + text2 + " 
  " + text3 + "
  " + text1 + ""
テキスト1: "正弦定理 
 " + (LaTeX[正弦定理]) + "
はいつでも成り立つのか！？
計算して確かめてみよう！"
テキスト2: " " + (LaTeX[text_1]) + "
 " + (LaTeX[text_2]) + "
 " + (LaTeX[text_3]) + "
  " + (LaTeX[text_4]) + ""