$5-$ A vertical curve connects a $-3\mathrm{.}5\%$ grade with a $+3\mathrm{.}5\%$ grade. The required nighttime headlight sight distance is $423$ ft $.$ The design vehicle's headlight is $2\mathrm{.}0$ ft from the pavement surface, with $=2$ degrees. Start by assuming $SL,$ work out the correct length of the curve.