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

Geometry Level 5

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
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