Trigonometry

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In a triangle ABC, if 2sinB=sinA+sinC and sides a+c=70, what is side b?

  • Trigonometry -

    b/sinB = a/sinA = c/sinC

    sinA/a = sinC/C
    sinA = a/c sinC
    sinA+sinC = (1+a/c) sinC
    = (a+c)/c sinC

    2sinB = sinA+sinC = 70/c sinC

    2b/2sinB = c/sinC
    2b = (70/c) sinC * c/sinC
    = 70
    b = 35

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