My question is very similar to this one, but I don't know how to modify the answer for an angle not relative to the origin. It's been way to long since math class.
If I have the line that passes through two points, lets say 1,3 and 5,3, and intersects a line at 5,3 with an angle θ, how do I calculate the slope of the second line? The formula given (tan(arctan(y/x)−θ)) assumes the angle has a relation to the x axis, but I need a more general formula.
This image should illustrate the case.
I have known line, and a point at which it intersects another line. If I know the angle formed by the two lines, how can I find the slope of the second line.
θ is given by $tan θ = | \frac {m – M} {1 + mM} |$
From θ = 100 degrees, tan θ is a known quantity H, say.
M, the slope of the line passing through (0, 10) and (10, 0) = … = –1
Therefore, $H = \frac {m + 1} {1 – m}$
:
$m = … = \frac {H – 1} {H + 1}$
Note: In case θ = 100 degrees, it is necessary to use the supplementary angle (80 degrees) instead to make sure that both sides are positive.