Results 1 to 8 of 8

Math Help - find angle between lines

  1. #1
    Member
    Joined
    Aug 2009
    Posts
    96

    find angle between lines

    find the acute angle between the lines:

    x - 2y + 1 = 0
    and
    y = 5x - 4
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by deej813 View Post
    find the acute angle between the lines:

    x - 2y + 1 = 0
    and
    y = 5x - 4
    1. x - 2y + 1 = 0 ~\implies~y=\frac12 x +\frac12

    y = 5x - 4

    2. The angle between the first line and the horizontal is \alpha. Then you know that \tan(\alpha) = \frac12 .

    The angle between the second line and the horizontal is \beta. Then you know that \tan(\beta) = 5 .

    3. The angle which is included by the 2 lines is (\beta - \alpha)

    4. Use the property:

    \tan(\beta - \alpha) = \dfrac{\tan(\beta) - \tan(\alpha)}{1+ \tan(\alpha) \cdot \tan(\beta)}

    5. Plug in the values you know. You should come out with: (\beta - \alpha) \approx 52.125^\circ
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member eXist's Avatar
    Joined
    Aug 2009
    Posts
    157
    Completely forgot about that identity, thanks Good to know.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Aug 2009
    Posts
    96
    ok thanks
    but what is that property that you used?
    how do you get it?
    how does it work?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by deej813 View Post
    ok thanks
    but what is that property that you used?
    This formula belongs to a set of equations concerning the trigonometric functions of sums (or differences) of angles.
    how do you get it?
    I learned it nearly 50 years ago - so I don't get it but I have it
    how does it work?
    Fine!
    As I've mentioned you only have to plug in the known values:

    \tan(\beta - \alpha) = \dfrac{5 - \frac12}{1+ 5 \cdot \frac12}= \dfrac{\frac92}{\frac72}=\dfrac97<br />

    Now you can calculate the angle using the \arctan- or tan^{-1} function.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Aug 2009
    Posts
    96
    ok then so its just a formula?
    is there another way to do it seen as i havnt learnt that yet or is this it?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by deej813 View Post
    ok then so its just a formula?
    is there another way to do it seen as i havnt learnt that yet or is this it?
    Of course there is.

    Solve for \alpha: \alpha = \tan^{-1} \frac{1}{2} (use a calculator).


    Solve for \beta: \beta = \tan^{-1} 5 (use a calculator).

    Calculate \beta - \alpha.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by deej813 View Post
    what is that property that you used?
    how do you get it?
    You don't have to remember the formula for \tan(\beta-\alpha), provided that you know the formulas for \sin(\beta-\alpha) and \cos(\beta-\alpha) (which are definitely things that are useful to remember). In fact \tan(\beta-\alpha) = \frac{\sin(\beta-\alpha)}{\cos(\beta-\alpha)} = \frac {\sin\beta\cos\alpha-\cos\beta\sin\alpha} {\cos\beta\cos\alpha+\sin\beta\sin\alpha}. Now divide top and bottom by \cos\beta\cos\alpha and you get the result \tan(\beta-\alpha) = \frac{\tan\beta-\tan\alpha}{1+\tan\beta\tan\alpha}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the angle between two straight lines
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: November 14th 2010, 04:50 PM
  2. angle between lines
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 10th 2010, 02:49 PM
  3. angle between lines
    Posted in the Algebra Forum
    Replies: 7
    Last Post: March 10th 2010, 01:40 PM
  4. Angle Between Two Lines
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 28th 2008, 03:00 PM
  5. cal the angle between the lines
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 12th 2008, 03:52 AM

Search Tags


/mathhelpforum @mathhelpforum