2026 NYGH P1 Q9

In the diagram, \(A\), \(B\), \(C\) and \(D\) are four food stall clusters set up along the Marina Bay waterfront promenade for the Singapore Food Festival. The food stall cluster at point \(B\) is due east of the food stall cluster at point \(A\). \(\angle DCB=107^\circ\), \(AB=26\text{ m}\) and \(DB=30\text{ m}\). The bearing of \(C\) from \(D\) is \(075^\circ\) and the bearing of \(B\) from \(D\) is \(130^\circ\).

1. Calculate
   1. the length \(CB\),[2]
   2. the area of \(\triangle DBA\).[2]
2. A decorative light tower of height \(11\text{ m}\) is to be set up at point \(X\) along the pathway from \(D\) to \(B\), such that the angle of elevation of the top of the light tower, as viewed from \(A\), is at its greatest. A stall manager claimed that the angle of elevation would not be greater than \(32^\circ\). Justify whether his claim is correct.[3]