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hu
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Calculate angles between two intersecting lines using the slopes

Asked by hu
on 14 Aug 2014
Latest activity Commented on by Amit Haldar on 6 Jan 2016
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

  1 Comment

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

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3 Answers

Answer by Roger Stafford on 14 Aug 2014
 Accepted 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.

  3 Comments

and what happend if I absolute the value?
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?

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Answer by Rick Rosson
on 14 Aug 2014

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

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Answer by Amir
on 14 Aug 2014

This image is from this video: https://www.youtube.com/watch?v=4bGt5wQf818
Hope this can clarify this for you.

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