Question # $1$:

A $2-$ lane road has a lane width of $3\mathrm{.}75m.$ It goes on a horizontal curve of degree of curvature $D=7\mathrm{.}16.$ The horizontal curve connects the tangents of a two$-$lane highway that has a posted speed limit of $56k\frac{m}{h}.$

a$)$ Determine the radius of the curve.

b$)$ If the highway curve is not super elevated, determine the horizontal sightline offset $($The minimum offset clearance$)$ that a large billboard can be placed from the centerline of the inside lane of the curve, without reducing the required Sight distance. Perception$-$reaction time is $2\mathrm{.}5sec,$ and the coefficient of friction between the road and the $f=0\mathrm{.}35$