Three deer, A$,$ B and C$,$ are grazing in a field. Deer B is located $62\mathrm{.}4$ m from deer A at an angle of $51\mathrm{.}3\backslash$deg north of west. Deer C is located $76\mathrm{.}7\backslash$deg north of east relative to deer A$.$ The distance between deer Band C is $92\mathrm{.}9$ m$.$ What is the distance between deer A and C$?$