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    In the attached figure they are looking for the values of X and Y I have been able to solve for the value of X as shown in the right triangle drawn but have been having trouble solving the value of Y.

    See the attached file.

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    Solution Preview

    See attachment.
    DE = x = 2.3343 (you have already solved) = DB + BF + FE
    => 2.3343 = DB + GH + FE
    but, FE = DB (by ...

    Solution Summary

    The solution assists with finding the values of X and Y in the right triangle drawn.