Question

derive an expression for the angle between two lines y1x

Answer 1

Answer:

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

Let the slope measurement can be taken as

tan a1 = m1 and 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 a2 as 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.

Step-by-step explanation:

Hope this is useful for you.