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Math Help - Inclination of path

  1. #1
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    Wink Inclination of path

    Hi guys!
    I am getting the wrong answer for the following question: a diagram is attached.
    A hillside forms a plane surface inclined at 25 \deg to the hoizontal. A straight path up the hillside makes an angle of 60 \deg with the line of greatest slope. Find to the nearest degree, the inclination of the path to the horizontal.

    I have: h = PQ = RS
    from \triangle ORS.
    tan 25 = h / OS
    OS = h / tan 25
    from \triangle OQS.
    cos 60 = OS/OQ
    OQ = OS / cos 60.
    OQ = h /(tan 25. cos 60)
    from \triangle OPQ. \tan \alpha = h / OQ = tan25. cos 60
    \alpha = tan^-1 (tan25. cos 60) = 13.1 \deg
    To the nearest degree this is 13.
    The answer I have in my maths book is 12 degrees.
    So, dear friends, am I wrong or is the book wrong?
    Attached Thumbnails Attached Thumbnails Inclination of path-m013.jpg  
    Last edited by s_ingram; November 3rd 2009 at 04:04 AM. Reason: Latex errors
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  2. #2
    Super Member
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    Jan 2009
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    My result is 13.1243 degrees.
    You are correct.
    The book has a typo.
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  3. #3
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    I was hoping someone would say that!
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