$\text{Trig! Or is it somethinge else?}$

A man of negligible height stands on a straight road. He observes that the $greatest$ $angle$ subtended on the road by two objects is $90^\circ$ . From this point, he walks a distance of $2km$ along the road. He then stops and observes the two objects form a $straight$ $line$ which subtends an angle of $30^\circ$ with the road. The distance between the two objects ( $in$ $km$ ) is $\frac {a}{ \sqrt { b} }$ . $\text{Find (a+b)}$ Details and Assumptions :

• $a$ and $b$ are co-prime

This question is part of the set Best of Me