geometry

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The bases of a trapezoid are 38 and 17 respectively. The angles at the extremities of the larger base are 57 degrees and 45 degrees. find the two legs.

  • geometry -

    The total base under the triangles is 21 (38-17)

    Let b = the base by the 57° angle

    So, the height

    h = b*tan 57 = (21-b) tan(45) = 21-b

    1.54b = 21-b
    b = 8.27
    21-b = 12.73

    h = 12.73

  • geometry -

    now, having the height, use either sine or cosine to find the legs.

  • geometry -

    6.65
    9.38

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