Two straights, $AI$ and $IB,$ whose bearings are $75{30}^{\text{'}}{30}^{\text{'}\text{'}}$ and $91{00}^{\text{'}}{30}^{\text{'}\text{'}}$ respectively intersect at I. A horizontal curve, comprising a central circular arc and two equal length transitions curve $($exit and entrance$),$ is to be used to connect these two straights. The chainage of I is $5151\mathrm{.}441$ metres while its coordinates are $,8892\mathrm{.}29mE).$ While, design speed and radius have been fixed at $90k\frac{m}{h}$ and $900m$ respectively. A rate of change of acceleration is $0\mathrm{.}3\frac{m}{s^3}.$

$($a$)$ Determine the length of the proposed combine curve and the running chainage of four tangent points and $($:$T_4\}.$

$(15$ marks$)$

$($b$)$ Prepare road curve setting out table for the first transition curve to $($:$T_2\}$ at $25m$ intervals.

$(15$ marks$)$

$($c$)$ During the road curve setting out, it was found that the location of the second running tangent $(T_2)$ is obstructed and not accessible from first running tangent $(($:$T_l\}.$ Supposing that the $T_2$ could be set out from I, calculate the required bearings and distances from I to $T_2.$

$(10$ marks$)$