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Math Help - angles between two lines

  1. #1
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    angles between two lines

    Happy New Year!

    There is a question on my exercise book that:

    The slopes of lines L1 and L2 are the roots of the equation 6 x^2 - 5x - 1 = 0

    If a is the acute angle between L1 and L2, find the value of tan a .


    The answer I 've calculated is 7 / 5.
    But the book says that it should be 1/7.
    How can I get this or it's the mistake of the book?
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  2. #2
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    Quote Originally Posted by ling_c_0202 View Post
    Happy New Year!

    There is a question on my exercise book that:

    The slopes of lines L1 and L2 are the roots of the equation 6 x^2 - 5x - 1 = 0

    If a is the acute angle between L1 and L2, find the value of tan a .


    The answer I 've calculated is 7 / 5.
    But the book says that it should be 1/7.
    How can I get this or it's the mistake of the book?
    The solutions to,
    6x^2-5x-1
    Are,
    x=\frac{5\pm \sqrt{25+24}}{12}

    x=\frac{5\pm 7}{12}
    Thus,
    x=1,-1/6

    The angle between two (non-perpendicular) lines is,
    \tan \theta = \frac{1+1/6}{1+(1)(-1/6)}
    Thus,
    \tan \theta = (7/6)(5/6)=1
    Thus,
    \tan \theta = 7/5
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  3. #3
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    Exactly the same as what I 've done. Thanks!
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