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Math Help - Law of Sines

  1. #1
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    Law of Sines

    Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

    B = 49, a = 16, b = 14

    Choices are

    A = 30.4, C = 100.6, c = 18.2; A = 149.6, C = 79.4, c = 18.2
    A = 30.4, C = 100.6, c = 10.7; A = 149.6, C = 79.4, c = 10.7
    A = 59.6, C = 71.4, c = 11.1; A = 120.4, C = 10.6, c = 11.1
    A = 59.6, C = 71.4, c = 17.6; A = 120.4, C = 10.6, c = 3.4
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  2. #2
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    Re: Law of Sines

    Do you know what the Law of Sines is?

    With the information you have been given, you should be able to calculate A.
    Then you should be able to calculate C, and c.

    Not sure how you can get another triangle from that information.
    Thanks from Shakarri
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  3. #3
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    Re: Law of Sines

    Hello, ambitionty9!

    Two triangles can be formed with the given information.
    Use the Law of Sines to solve the triangles.

    . . B = 49^o,\;a=16,\;b=14


    [1]\;A = 30.4^o,\;C = 100.6^o,\;c = 18.2
    . . A = 149.6^o,\;C = 79.4^o,\;c = 18.2

    [2]\;A = 30.4^o,\;C = 100.6^o,\;c = 10.7
    . . A = 149.6^o,\;C = 79.4^o,\;c = 10.7

    [3]\;A = 59.6^o,\;C = 71.4^o,\;c = 11.1
    . . A = 120.4^o,\;C = 10.6^o,\;c = 11.1

    [4]\;A = 59.6^o,\;C = 71.4^o,\;c = 17.6
    . . A = 120.4^o,\;C = 10.6^o,\;c = 3.4

    Law of Sines: . \frac{\sin A}{a} \,=\,\frac{\sin B}{b} \quad\Rightarrow\quad \sin A \,=\,\frac{a\sin B}{b}

    We have: . \sin A \:=\:\frac{16\sin49^o}{14} \:=\:0.862525235

    Hence: . A \:=\:59.60130951 \quad\Rightarrow\quad \boxed{A \:\approx\:59.6^o} . **

    Then: . C \:=\:180^o - 49^o - 59.6^o \quad\Rightarrow\quad \boxed{C \:=\:71.4^o}

    Law of Sines: . \frac{c}{\sin C} \,=\,\frac{b}{\sin B} \quad\Rightarrow\quad c \:=\:\frac{b\sin C}{\sin B}

    We have: . c \:=\:\frac{14\sin71.4^o}{\sin49^o} \:=\:17.58127641 \quad\Rightarrow\quad \boxed{c \:\approx\:17.6}


    ** .We also have: . \boxed{A \:=\:120.4^o}

    Then: . C \:=\:180^o - 49^o - 120.4^o \quad\Rightarrow\quad \boxed{C \:=\:10.6^o}

    We have: . c \:=\:\frac{14\sin10.6^o}{\sin29^o} \:=\:3.412331016 \quad\Rightarrow\quad \boxed{c \:=\:3.4}


    Therefore: answer choice [4]
    Thanks from abualabed
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