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Math Help - Cos rule question

  1. #1
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    Cos rule question

    I got this question, I know how to do it but the answer is never right

    A weight is hung from two hooks in a ceiling by strings
    of length 54 cm and 42 cm, which are inclined at 70◦ to
    each other. Find the distance between the hooks.

    c^2 = 54^2+42^2 -(2)(54)(42) \cos 70

    Is this right?
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  2. #2
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    I believe it looks good.
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  3. #3
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    Alright,

    For this:

    It asks me to find CD. I've been trying ages but I have no idea how to do it. Can someone help me out?
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  4. #4
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    Use the law of cosine to solve BD.

    a^2=4^2+6^2-2*4*6*cos(92)\Rightarrow a=7.326=BD

    Now use the law of sine to solve the angle BDC.

    \displaystyle \frac{sin(88)}{7.326}=\frac{sin(BDC)}{5}\Rightarro  w BDC=sin^{-1}\left(\frac{5sin(88)}{7.326}\right)=43.0043

    angle DBC = 180-88-43.0034=48.9957

    law of sine to solve DC

    \displaystyle \frac{sin(88)}{7.326}=\frac{sin(48.9956)}{DC}\Righ  tarrow DC=\frac{7.326*sin(48.9957)}{sin(88)}=5.5323
    Last edited by dwsmith; December 19th 2010 at 08:21 PM.
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  5. #5
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    OMG!!! I'm so stupid!!!!

    (sigh) I better keep practising these

    Thanks a lot!
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