A level rural two$-$lane road has a $12-$degree curved section as it passes by a large building. The obstruction corner of the building is $24\mathrm{.}0$ ft away from the centerline of the highway.

a$)$ Assume the degree of curve is referenced to the centerline of the roadway. What is radius of the centerline of the roadway?

b$)$ If the lanes of the highway are $12$ ft wide, what is the current sight distance on this section?

c$)$ This building is being remodeled and the architect has requested a variance to the zoning that would allow this obstructing corner to be $15\mathrm{.}1$ ft from the centerline of the highway. Your boss has asked you to evaluate how this change affects the sight distance. She is specifically wants to know:

i$)$ What is the safe speed limit on this section before and after the proposed change to the building?

ii$)$ If the speed limit for the road is $40$ mph$,$ should the variance be granted