$(35$ points$)$ Given the closed Trigonometric leveling data below, calculate the error of closure, classify the error, and the corrected elevations.

$\backslash$table$[[$Sta$/$Pos$,$BS$,$BD$,$FS$,$FD$,\backslash$Delta Elev.,Elev.$],[$A$,,,,,,2042659($known$)],[,8\mathrm{.}567,267\mathrm{.}331,10\mathrm{.}425,255\mathrm{.}981,,],[$B$,,,,,,],[$C$,4\mathrm{.}726,222\mathrm{.}754,5\mathrm{.}337,237\mathrm{.}672,,],[$D$,,,,,,],[$A$,6\mathrm{.}773,178\mathrm{.}623,13\mathrm{.}673,187\mathrm{.}624,,]]$