$($a$)$ Two straights, $AI$ and $IA,$ whose bearings are $50$ and $85$ respectively intersect at I, are to be connected by a combined curve. The chainage of I is $6634$ metres while its coordinates are $(52388\mathrm{.}75m$ N$,39892\mathrm{.}29$m E$).$ The design speed and radius have been fixed at $75k\frac{m}{h}$ and $350m$ respectively. Adopting a rate of change of acceleration of $0\mathrm{.}3\frac{m}{s^3},$ prepare the setting out table $($to nearest $cm)$ for the FIRST transition only at $20m$ intervals.

$(20$ marks$)$

$($b$)$ During setting out, it was found out that the location of the first running tangent $($Ti$)$ is obstructed and not accessible. Supposing that the curve could be set out from I, calculate the required bearings and distances from I of the first four points on the FIRST transition.

$(20$ marks$)$

$(40$ marks$)$