$1.$ A highway is being designed to AASHTO specifications with a $55-$mph design speed as an equal tangent vertical curve to connect grades of $+1\mathrm{.}0\%$ and $-1\mathrm{.}5\%.$ For both stopping sight distance $($SSD$)$ and passing sight distance $($PSD$),(1)$ calculate the required sight distance $($assuming no grade$),(2)$ calculate the required length assuming L$>$S$,(3)$ calculate the required length using L