2025 AHS PRELIMS P1 Q14

In the diagram, \(PQ=25\text{ cm}\), \(QR=7\text{ cm}\) and \(\angle SRP=90^\circ\). \(QRST\) is a straight line.

1. Given that \(\sin\angle TSP=\dfrac45\), find the exact value of
   1. \(\cos\angle TSP\),[1]
   2. the length of \(SR\).[3]
2. A triangle with vertices \(ABC\) has an area of \(16.9\text{ cm}^2\). \(AB=8.9\text{ cm}\) and \(AC=4.7\text{ cm}\). Find the two possible values of angle \(BAC\).[2]