Thread: Basic coordinate geometry formula to find the angle between two lines

I just read that the angle between two lines with gradients m' and m'' can be found by:

tan(angle) = (m'' - m')/(a+(m'm''))


In try to prove this I saw that the angle can also be found by:

angle = invtan(m'') - invtan(m') which seems much simpler


Is this correct and if so why would we bother with the first formula?

Originally Posted by kinhew93

I just read that the angle between two lines with gradients m' and m'' can be found by:

tan(angle) = (m'' - m')/(a+(m'm''))

I think what you meant to write is this:


Hence:


And as yuo point out you can also use:


Both equations are equivalent. Use whichever you like, but I agree that the second form is more intuitively obvious.

Originally Posted by kinhew93

I just read that the angle between two lines with gradients m' and m'' can be found by:
tan(angle) = (m'' - m')/(a+(m'm''))
In try to prove this I saw that the angle can also be found by:
angle = invtan(m'') - invtan(m') which seems much simpler
Is this correct and if so why would we bother with the first formula?

Consider two simple lines: .

Now test your conclusion on those lines.

What do you get?