A horizontal curve is designed for a two$-$lane road in mountainous terrain. The following data are known: $(30\%)$

Deflection angle: $25$ degrees

Tangent length: $435\mathrm{.}08$ feet

Station of PI: $150+20\mathrm{.}63$

$f_s=0\mathrm{.}12$

$e=0\mathrm{.}08$

Determine the following:

$($a$)$ Design speed

$($b$)$ Station of the PC

$($c$)$ Station of the PT