# tan A

• Oct 30th 2009, 10:18 AM
Aquafina
tan A
Let L1 and L2 be two lines in the plane, with equations y = m1x + c1 and y = m2x + c2 respectively. Suppose that they intersect at an acute angle A. Show that

tan A = (m1-m2)/(1+m1m2) <-- modulus of this

The lines and modulus shows that I should use the formula for cos A with the dot product etc. But I am not sure what the dot product will be.

Any hints?
• Oct 30th 2009, 01:04 PM
Hello Aquafina
Quote:

Originally Posted by Aquafina
Let L1 and L2 be two lines in the plane, with equations y = m1x + c1 and y = m2x + c2 respectively. Suppose that they intersect at an acute angle A. Show that

tan A = (m1-m2)/(1+m1m2) <-- modulus of this

The lines and modulus shows that I should use the formula for cos A with the dot product etc. But I am not sure what the dot product will be.

Any hints?

This is a very similar question to this one. Use the same method as I have done there, and the result follows immediately. (Don't try to use dot product!)