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Pre-Calc Helppp!!!

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Find the indicated angle è.
(Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 110 and c = 136 (angle B=38)
Round your answer to two decimal places.)

  • Pre-Calc Helppp!!! - ,

    Law of Cosines:

    cosB = (a^2+c^2-b^2)/2ac.
    cos38 = ((110)^2+(136)^2-b^2) / 29920.
    0.7880 = (30596-b^2) / 29920.
    Cross multiply:
    30,596-b^2 = 0.7880*29920 = 23576.96.
    -b^2 = 23,976.96-30596 = -6619.04.
    b^2 = 6619.04.
    b = 81.36.

    Law of Sines:

    sinA/a = sinB/b.
    sinA / 110 = sin38 / 81.36.
    Multiply both sides by 110:
    sinA = 110(sin38 / 81.36) = 0.832384.
    A = 56.34 Deg.

    C = 180 - 38 - 56.34 = 85.66 Deg.

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