## Calculate angles between two intersecting lines using the slopes

### hu (view profile)

on 14 Aug 2014
Latest activity Commented on by Amit Haldar

on 6 Jan 2016

### Roger Stafford (view profile)

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

Amit Haldar

### Amit Haldar (view profile)

on 6 Jan 2016
Yes that is how we calculate the angle between two lines.

### Roger Stafford (view profile)

on 14 Aug 2014

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.

hu

### hu (view profile)

on 14 Aug 2014
and what happend if I absolute the value?
Roger Stafford

### Roger Stafford (view profile)

on 14 Aug 2014
Correction: If you take the absolute value of (m1-m2)/(1-m1*m2) it can still give a negative angle. If you take the absolute value of value from atand, it will give you the positive angle between the lines which does not exceed 90 degrees. Is the latter what you were asking?
hu

on 15 Aug 2014
yep

### Rick Rosson (view profile)

on 14 Aug 2014

phi = atan(m1) - atan(m2);