2026 CCHMS P1 Q17

The points \(P(p,0)\) and \(R(p,6)\) are shown in the diagram. Point \(Q\) lies on the \(x\)-axis while point \(S\) lies on the \(y\)-axis.

1. Explain clearly why triangle \(OPR\) is a right-angled triangle.[1]
2. It is given that \(\cos\angle ROQ=-\dfrac45\).
   Without using a calculator, find
   1. the value of \(p\),[3]
   2. the value of \(\tan\angle ROS\).[1]