Line-Line Angle
For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by
The angle theta between two lines in the plane specified in trilinear coordinates by
lalpha+mbeta+ngamma =
(2)
l^'alpha+m^'beta+n^'gamma =
(3)
is given by
| tantheta=y/x, |
(4)
|
where
x=ll^'+mm^'+nn^'-(mn^'+m^'n)cosA-(nl^'+n^'l)cosB-(lm^'+l^'m)cosC
(5)
y=(mn^'-m^'n)sinA+(nl^'-n^'l)sinB+(lm^'-l^'m)sinC
(6)
(Kimberling 1998, p. 31).
See also
Line-Line Distance, Line-Line Intersection, Trilinear LineExplore with Wolfram|Alpha
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References
Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Referenced on Wolfram|Alpha
Line-Line AngleCite this as:
Weisstein, Eric W. "Line-Line Angle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Line-LineAngle.html