A crest vertical curve connects a $+4\mathrm{.}90$ percent grade and a $1\mathrm{.}85$ percent grade. The PVI is at station $77+00\mathrm{.}00$ at an elevation of $372$ m$.$ The design speed is $96$ km$/$h$.$Determine: $($a$)$ The length of the vertical curve using the AASHTO method $($K$$ factors$)$

$($b$)$ The station of the BVC

$($c$)$ The elevation of the BVC

$($d$)$ The station of the EVC

$($e$)$ The elevation of the EVC

$($f$)$ The station of the high point

$($g$)$ The elevation of the high point

$($h$)$ The elevation of station $75+09\mathrm{.}00$