A horizontal curve on a level two$-$lane highway is designed with $500m$ radius, $3\mathrm{.}6m$ wide lanes, and $90k\frac{m}{h}$rspeed. The highway section is $2\%$ upgrade, the coefficient of friction is $0\mathrm{.}30,$ and the perception$-$reaction time is $2\mathrm{.}5sec.$ Perform the following task:

a$)$ Determine the required stopping sight distance.

$(10$ Points$)$

b$)$ Determine the required horizontal sightline offset.

$(10$ Points$)$

c$)$ Draw a sketch showing the distance that needs to be cleared from the inside edge of the inside lane to provide sufficient stopping sight distance. $(5$ Points$)$