construct a triangle XYZ in which |YZ|=6 cm angle XYZ=60° and |XZ|=9 cm measure|XY| , construct a mediator of XY and draw a circle with center X and a radius of 5cm. Measure|YA|, where A is the point of intersection of the mediator and the circle in the triangular region XYZ

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  1. sin60°/9 = sinX/6
    X = 35.3°
    So, Z = 84.7°
    XY/sin84.7° = 9/sin60°
    XY = 10.35

    not sure what a mediator XY is
    you mean the median from Z to XY?
    Since XY is just about exactly 10, the circle will touch XY pretty much at its center.

    Maybe a bit of explanation is in order. Or maybe, knowing all the sides, you can finish up yourself.

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