MATLAB: Calculate angles between two intersecting lines using the slopes

angleslope

Hi,
I have two slopes M1 and M2 that I wish to check the angle between them.
I was told that I can use the inverse tangent of (m1 – m2)/(1 + m1*m2)
atand((m1-m2)/(1-m1*m2))
Is it true, why? What is the difference if I use the (m1 – m2)/(1 – m1*m2) instead?
Thanks

Best Answer

That formula comes from the trigonometric identity
   tan(A-B) = (tan(A)-tan(B))/(1+tan(A)*tan(B))
Note: You have the sign wrong in atand((m1-m2)/(1-m1*m2))
It should be understood that taking the arctangent (atand) of your expression corresponds to rotating the line with slope m2 in both a counterclockwise and a clockwise direction around the intersection point until first encountering the line with slope m1. Going counterclockwise counts as a positive angle and clockwise is considered negative. Therefore your answer will lie between +90 and -90.
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