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Math Help - Law of Sines problem (SSA)

  1. #1
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    Law of Sines problem (SSA)

    The question reads:

    Solve triangle ABC if A = 75, a = 5, and b = 7.
    a) B = 43.6, C = 61.4, c = 6.4
    b) B = 136.4, C = 31.6, c = 2.7
    c) B = 46.4, C = 58.6, c = 4.4
    d) no solution

    First, I try to solve for angle B:
    <br />
\frac {a} {\sin A} = \frac {b} {\sin B}<br />

    <br />
\frac {5} {\sin75} = \frac {7} {\sin B}<br />

    <br />
5 \sin B = 7\sin 75<br />

    <br />
\sin B = \frac {7sin 75} {5}<br />

    <br />
\sin B = 1.3523<br />

    <br />
\sin^-1 (1.3523) = Undefined


    So is the answer "No Solution"? Or, did I make a mistake?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by AlderDragon View Post
    The question reads:

    Solve triangle ABC if A = 75, a = 5, and b = 7.
    a) B = 43.6, C = 61.4, c = 6.4
    b) B = 136.4, C = 31.6, c = 2.7
    c) B = 46.4, C = 58.6, c = 4.4
    d) no solution

    First, I try to solve for angle B:
    <br />
\frac {a} {\sin A} = \frac {b} {\sin B}<br />

    <br />
\frac {5} {\sin75} = \frac {7} {\sin B}<br />

    <br />
5 \sin B = 7\sin 75<br />

    <br />
\sin B = \frac {7sin 75} {5}<br />

    <br />
\sin B = 1.3523<br />

    <br />
\sin^-1 (1.3523) = Undefined


    So is the answer "No Solution"? Or, did I make a mistake?
    I get an answer of no solution too using the sine rule
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  3. #3
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    skeeter's Avatar
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    North Texas
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    Quote Originally Posted by AlderDragon View Post
    The question reads:

    Solve triangle ABC if A = 75, a = 5, and b = 7.
    a) B = 43.6, C = 61.4, c = 6.4
    b) B = 136.4, C = 31.6, c = 2.7
    c) B = 46.4, C = 58.6, c = 4.4
    d) no solution
    in the ambiguous case, for a triangle to exist, the following inequality must be true ...

    a \ge b\sin{A}

    note that b\sin{A} = 7\sin(75) = 6.76 > 5

    no triangle is possible
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  4. #4
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    Quote Originally Posted by skeeter View Post
    in the ambiguous case, for a triangle to exist, the following inequality must be true ...

    a \ge b\sin{A}

    note that b\sin{A} = 7\sin(75) = 6.76 > 5

    no triangle is possible
    Thank you! That clears it up
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