Question

Derive an expression for the acute angle between two lines having slopes m1 and m2 and hence find the acute angle between the lines x+y-6=0 and x-y-5=0​

Answer 1

Answer:

tanθ=±(m2-m1) / (1+m1m2)

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

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

tanθ= (m2 – m1 ) / (1+m1m2)