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Angle between two lines.

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In a plane when two non-parallel straight lines intersect each other, it forms two opposite vertical angles. One of them is acute i.e. less than 90 degrees and the other one is obtuse that is more than 90 degrees. We will be calculating the angle between two non-perpendicular lines as the angle between two perpendicular lines would be 90 degrees and that of parallel lines will be zero. Finding the value of these angles depend on the slopes formed by the intersecting lines.

Formula to Find the Angle Between Two Lines:

Consider two nonparallel lines which have slopes m1 and m2 and θ is the angle between the lines, then the formula for finding the angle between the two lines would be:

tanθ =(m2-m1)/(1+m1m2)

Angle Between Two Straight Lines Derivation:

In the diagram above, the line L1 and line L2  intersect at a point.

Let the slope measurement can be taken as

tan a1 = mand tan a2 = m2

Also, from the figure, we can infer that θ = a2-a1

Now, tan θ = tan (a2-a1) = (tan a2 – tan a1 ) / (1- tan a1tan a2)

Substituting the values of tan a1 and tan aas m1 and m2 respectively, we have,

tanθ= (m2 – m1 ) / (1+m1m2)

It should be noted that the value of tan θ in this equation will be positive if θ is acute and negative if θ is obtuse.

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