$3)$ A road has a $55$ mph design speed. It has a vertical curve that goes from $+6\%$ to $-3\%.$ The PVC is at station $43+00$ and elevation $450$ ft$.$ Calculate the:

a$)$ PVT station $[1$ point$]$

b$)$ PVT elevation $[1$ point$]$

c$)$ Minimum curve length required for sight distance using AASHTO assumptions. Is the curve long enough? $[1$ point$]$