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Math Help - Basic coordinate geometry formula to find the angle between two lines

  1. #1
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    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?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Basic coordinate geometry formula to find the angle between two lines

    Quote Originally Posted by kinhew93 View Post
    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:
     \tan(a) = \frac {m''-m'}{1 + m'm''}

    Hence:
    a = arctan(\frac {m''-m'}{1 + m'm''} )

    And as yuo point out you can also use:
     a = arctan(m') - arctan(m'')

    Both equations are equivalent. Use whichever you like, but I agree that the second form is more intuitively obvious.
    Last edited by ebaines; December 10th 2012 at 09:42 AM.
    Thanks from kinhew93
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  3. #3
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    Re: Basic coordinate geometry formula to find the angle between two lines

    Quote Originally Posted by kinhew93 View Post
    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: y=3x~\&~y=-5x.

    Now test your conclusion on those lines.

    What do you get?
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