Angle between two lines

show line

tan\,θ = \left| {\frac{m_1-m_2}{1+m_1m_2}} \right|

show line2

show angles

show gradients

show formula

a1 = 1 (slider from -5 to 5, step 0.5)
b1 = -1 (slider from -5 to 5, step 0.5)
c1 = 3.5 (slider from -10 to 10, step 0.5)
l_1: a1 * x + b1 * y + c1 = 0.0
x1 = NaN (slider from -5 to 5, step 1)
y1 = NaN (slider from -5 to 5, step 1)
P: (x1, y1)
d = OrthogonalLine(P, l_1)
A_1 = Intersect(l_1, d)
f_1 = Segment(A_1, P)
g = true
a2 = -1 (slider from -5 to 5, step 0.5)
b2 = -0.5 (slider from -5 to 5, step 0.5)
c2 = 3.5 (slider from -10 to 10, step 0.5)
l_2: a2 * x + b2 * y + c2 = 0.0
B_1 = Intersect(xAxis, yAxis)
C_1 = Point(xAxis)
a = Line(B_1, C_1)
A = Intersect(l_1, l_2)
B = Intersect(l_1, a)
C = Intersect(l_2, a)
α = Angle(C, B, A)
θ = Angle(B, A, C)
G = Point(a)
β = Angle(G, C, A)
text3: "m_1 = tan(" + α + ")"
text4: "m_1 = " + (tan(α))
text5: "m_2 = tan(" + β + ")"
text6: "m_2 = " + (tan(β))
m_1: tan(α)
m_2: tan(β)
text7: "tan\,θ = \left| {\frac{" + m_1 + "-" + m_2 + "}{1+" + m_1 + " × " + m_2 + "}} \right|"
text8: "tan\,θ = \frac{" + (abs(m_1 - m_2)) + "}{" + (abs(1.0 + m_1 * m_2)) + "}"
text9: "θ\,=\,tan^{-1}\left(\frac{" + (abs(m_1 - m_2)) + "}{" + (abs(1.0 + m_1 * m_2)) + "}\right)"
text10: "θ\,=\," + ((atan(abs(m_1 - m_2) / abs(1.0 + m_1 * m_2)) * 180.0 / 3.141592653589793)°)
b = true
c = true
e = true
f = true