2025 YCKSS PRELIMS P2 Q5

A harbour \(H\) and islands \(A,B,C\) satisfy \(HA=5.4\) km, \(AB=3.1\) km, \(AC=6.5\) km, bearing of \(A\) from \(C\) is \(133^\circ\), \(\angle HAB=128^\circ\), and \(C\) is due north of \(H\).

1. Calculate \(HB\).[2]
2. Show that \(\angle CAH=71.3^\circ\), correct to one decimal place.[3]
3. Find the bearing of B from A.[2]
4. A vertical tower stands on A. Its top has elevation \(14^\circ\) from B. Calculate its elevation from C.[3]