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Math Help - Law of Cosines - Negative angle??

  1. #1
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    Law of Cosines - Negative angle??

    Here's the triangle:


    a=8
    b=3
    c=8

    I did the law of cosines for C and got 0.1875. I did the arccos of that, and got 79.19.

    I then did the law of sines for A, and got 2.62444. I did the arcsin of that, and got undefined on my TI-89. I put arcsin(2.62444) in WolframAlpha and got -45.88.

    So... Am I doing something wrong?
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  2. #2
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    Quote Originally Posted by BeSweeet View Post
    Here's the triangle:


    a=8
    b=3
    c=8

    I did the law of cosines for C and got 0.1875. I did the arccos of that, and got 79.19.

    I then did the law of sines for A, and got 2.62444. I did the arcsin of that, and got undefined on my TI-89. I put arcsin(2.62444) in WolframAlpha and got -45.88.

    So... Am I doing something wrong?
    I got the same thing for angle C. The law of sines is that a/sinA =c/sinC. Since a and c are the same length their angles must be equal. I don't know where you made your error since you didn't post your work but angle C is definitely 79.19 as well.
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  3. #3
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    angle A = angle C, no?
    since a=c

    therefore it would have the same angle.

    duno how you got 2.62444.

    \frac{sin79.19}{8}=\frac{sinA}{8}

    \frac{sin79.19}{8}*8=sinA

    \rightarrow sin79.19=sinA

    therefore A=79.19.

    btw dont trust WolframAlpha
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  4. #4
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    So what do I need to do? I've already found one angle, and I can't find the other two...
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  5. #5
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    Quote Originally Posted by BeSweeet View Post
    So what do I need to do? I've already found one angle, and I can't find the other two...
    Like we said, the law of sines should show that the angles opposite the legs with length of 8 are the same. The total angle measure of a triangle is 180, so if you know 2 angles you can find the third.
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  6. #6
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    I did the law of sines but couldn't get an angle...
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  7. #7
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    Quote Originally Posted by BeSweeet View Post
    So what do I need to do? I've already found one angle, and I can't find the other two...
    use the sine rule to find B,

    \frac{sin79.19}{8}=\frac{sinB}{3}

    rearrange to find B.

    alternatively you can do 180-79.19-79.19

    since triangle =180 degrees

    there you have your ABC

    where

    A=79.19
    B=21.61
    C=79.19
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  8. #8
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    Quote Originally Posted by BeSweeet View Post
    I did the law of sines but couldn't get an angle...
    I can't help fix your error without your work. Look at the setup:

    sin79.19/8=sinA/8

    Both sides have the exact same form and the same denominator. So they must have the same numerator meaning angle a=c.
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