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geometry

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In Triangle ABC, AD is median. If AB is 8, BC is 18, AD is 7, find AC

  • geometry - ,

    Since AD is the median
    BD = DC = 9
    In ∆ABD, let ∢BDA = Ø
    by the cosine law:
    8^2 = 9^2 + 7^2 - 2(9)(7)cosØ
    cosØ = .5238
    Ø = 58.4°
    the ∢ADC = 121.59°

    now in ∆ADC
    AC^2 = 49 + 64 - 2(7)(8)cos121.59
    = 171.666667
    AC = 13.102 or 13

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