2026 AHS P1 Q7

The diagram shows a triangle \(PQR\) in which \(PQ=4\text{ cm}\), \(QR=2\text{ cm}\) and \(\angle PQR=30^\circ\).

The point \(S\) lies on the line \(QR\) produced such that \(\angle PSR=90^\circ\).

1. Express \(PR^2\) in the form \(a+b\sqrt3\), where \(a\) and \(b\) are constants.[2]
2. Show that \(\angle PRS=\tan^{-1}\left(\dfrac{\sqrt3+1}{2}\right)\).[4]