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Math Help - Three known sides need angles

  1. #1
    Junior Member Jarod_C's Avatar
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    Three known sides need angles

    a=152.4cm b=same c=118.11cm Now I need the angles.

    I'm building a chicken coop and can't figure out the the angles. I guess two semesters of algebra and trig two years ago doesn't do me any good now if I don't remember any of it. I think the problem is not remembering my calculator functions. I got 0.3875 for A, and I think I just need to hit COS but when I do it doesn't sound right. Maybe I'm way off. Anyway if someone could show their work I'd like to know where I went wrong.


    Thanks alot for the help.

    Edit:I'll try to show my work below to see where I went wrong.

    (b^2+c^2-a^2)/2bc=\cos A
    ,so
    (13949.9721)/35999.928=0.3875
    Last edited by Jarod_C; April 9th 2010 at 09:21 AM. Reason: showing work
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  2. #2
    Senior Member
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    The law of cosines will help.

    c^2 = a^2 + b^2 - 2ab cos (\theta)

    a,b,c are the sides of the triangle. From there you can get cos(theta) and from there get theta.
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  3. #3
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    Hello, Jarod_C!

    Your work is correct . . . take it a step further.


    a \:=\: b\:=\:152.4\text{ cm,}\;c\:=\:118.11\text{ cm}
    Find angles A,B,C.


    I'll try to show my work below to see where I went wrong.

    \cos A \:=\:\frac{b^2+c^2-a^2}{2bc}

    So: . \cos A \:=\:\frac{13949.9721}{35999.928} \:=\:0.3875

    Then: . A \;=\;\cos^{-1}(0.3875) \:=\:67.20096873^o \quad\Rightarrow\quad \boxed{A \;\approx\;67.2^o}

    The triangle is isosceles, so: . \boxed{B \:=\:67.2^o}

    Hence: . C \;=\;180^o - 67.2^o - 67.2^o \quad\Rightarrow\quad \boxed{C\:=\:45.6^o}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    Check

    \cos C \:=\:\frac{152.4^2 + 152.4^2 - 118.11^2}{2(152.4)^2} \;=\;0.6996875

    Therefore: . C \:=\:45.59806254^o \quad\Rightarrow\quad \boxed{C \;\approx\; 45.6^o}

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  4. #4
    Junior Member Jarod_C's Avatar
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    Tyvm, that's what I was needing. I'm still stumped on my calculator though. What function changes decimal from 0.3875 to 67.2^o

    I think I'm going to lay off the ps3 because I used to be able to do this in my sleep.

    Edit:LOL I'm rusty at this. I got my function by reading the problem. 03875 cos-1 = 67.2 deg. Thanks it really helped.
    Last edited by Jarod_C; April 9th 2010 at 11:37 AM.
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