Math: law of cosines, hw help?

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  • 5 months ago
    Favorite Answer

    Apply the law of cosine

    ∠B = 180 - 111 = 69°

    solving for side b

    b = √[a^2 + c^2 - 2accos(B)]

    b = √[19^2 + 10^2 - 2(19)(10)cos(69)]

    b = 18.022 or 18

    apply law of sine to solve Angle C

    .....b..............c

    --------- =-----------

    ..sin(B)....sin(C)

    ...18.............10

    ----------- =---------

    ..sin(69)...sin(C)

    18sin(C) = 10sin(69)

    ................10sin(69)

    sin(C) = ----------------- <-----------closest answer on choice D

    .......................18

    ...................................10sin(69)

    Answer is D. sin(C) =---------------

    .......................................19

  • 5 months ago

     In △ABC, a = 19, c = 10, and m∠A = 111°. 

     Which statement can be used to find the value of C?

     The Law of Cosines (also called the Cosine Rule) says: 

      a^2 = b^2 + c^2 − 2bc cos (A)

     19^2 = b^2 + 10^2 - 20b cos (111°)  

      b(b - 20 cos (111°) = 29*9

      b (b + 20 sin((7 π)/60)) = 261

  • fcas80
    Lv 7
    5 months ago

    Law of Sines:  sinC/10 = sin111/19

    sinC=10 * sin111 / 19.  But sin111 = sin69

    sinC = 10 * sin69 / 19

    answer D

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