2026 TPSS P2 Q7

In the diagram, \(P\), \(Q\), \(R\) and \(S\) are four points on horizontal ground.

\(QR=520\text{ m}\), \(RS=300\text{ m}\), \(PS=980\text{ m}\), angle \(QRS=110^\circ\) and angle \(QPS=42^\circ\).

1. Show that \(QS\approx683.455\text{ m}\).[2]
2. Calculate angle \(PSQ\).[3]
3. Find the shortest distance from \(Q\) to the line \(PS\).[2]
4. A drone flies at a height of 1 km above the line \(SP\). Find the greatest angle of elevation when viewed from \(Q\).[2]