$$

Question $1(20$ points$)$: A horizontal curve is to be designed for a two$-$lane road in mountainous terrain. The following data are known: Intersection angle: $40$ degrees, tangent length $=500ft,$ station of PI: $270+00,$ fs $=0\mathrm{.}15,e=0\mathrm{.}06.$

Determine:

$($a$)$ design speed $(10$ points$)$

$($b$)$ station of the PC $(5$ points$)$

$($c$)$ station of the PT $(5$ points$)$

Please show design speed calc thank you