Three deer, A$,$ B$,$ and C$,$ are grazing in a field. Deer B is located $60\mathrm{.}4$ m from deer A at an angle of $52\mathrm{.}9\backslash$deg north of west. Deer C is located $75\mathrm{.}7\backslash$deg north of east relative to deer A$.$ The distance between deer B and C is $97\mathrm{.}6$ m$.$ What is the distance between deer A and C$?$