Calculate angles between two intersecting lines using the slopes

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]

Yes that is how we calculate the angle between two lines.

Answer 1

[Roger Stafford]

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]

and what happend if I absolute the value?

[Roger Stafford]

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]

yep

Answer 2

[Rick Rosson]

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

Answer 3

[Amir]

This image is from this video: https://www.youtube.com/watch?v=4bGt5wQf818

Hope this can clarify this for you.