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Thread: Law of Cosines - SAS

  1. #1
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    Law of Cosines - SAS

    So, I am given SAS.

    Now I must find the remaining angles and side.

    I am given:

    M<A=
    M<B=20 degrees
    M<C=
    a=10mm
    b=
    c=15mm

    and the triangle looks somewhat like this:

    ......10mm
    B\---------|C
    ...\20........|
    ....\...........|
    .....\..........|
    ......\.........|
    .......\........|
    ........\.......|
    15mm.\......|
    ..........\.....|
    ...........\....|
    ............\...|
    .............\..|
    ...............A
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Law of Cosines - SAS

    First use the law of cosines to find the length of b. Then use the law of sines to find the angle A, and finally angle C. Post back with what you get for answers and we'k check it for you.
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  3. #3
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    Re: Law of Cosines - SAS

    Quote Originally Posted by ebaines View Post
    First use the law of cosines to find the length of b. Then use the law of sines to find the angle A, and finally angle C. Post back with what you get for answers and we'k check it for you.
    Ah! Well, b is ~ 4.85. Then, I did as you said with the law of sines to find that M<A is 44.85 degrees, and M<C is 115.15 degrees.

    Is that correct?
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: Law of Cosines - SAS

    I get b = 6.56mm. Using the law of cosines:

    b^2 = a^2 + c^2 - 2ac \cos(b) = 10^2 + 15^2 - 2(10)(15)(0.9397) = 43.09 , so b = 6.56
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