Here PQ = 1

Plz see the diagram attached.

Now △ PQT,

∠QPT = 30° , ∠QTP = 90° and ∠PQT = 60°

so it is a 30° - 60° -90° and we know the sides are distributed in the ratio \(1 : \sqrt3 : 2\)

Now PQ = 1,
so \(QT = \frac{1}{2} and PT = \frac{2}{sqrt3}\)

Now let us consider △ QTS


∠TQS = 30° , ∠QST = 60° and ∠QTS = 90°
so it is a 30° - 60° -90° and we know the sides are distributed in the ratio \(1 : \sqrt3 : 2\)

Now \(QT = \frac{1}{2}\),
so \(QS = \frac{1}{\sqrt3} and TS = \frac{1}{2\sqrt3}\)

Now let us consider △ TRS


∠RST = 60° , ∠RTS = 30° and ∠TRS = 90°
so it is a 30° - 60° -90° and we know the sides are distributed in the ratio \(1 : \sqrt3 : 2\)

Now \(TS = \frac{1}{2\sqrt3}\),
so \(RT = \frac{1}{4} and RS = \frac{1}{4\sqrt3}\).

But \(RS = \frac{1}{4\sqrt3}\) can also be written as \(RS = \frac{1}{4\sqrt3} *\frac{\sqrt3}{\sqrt3} = \frac{\sqrt3}{12}\)