2025 AHS PRELIMS P2 Q12

The diagram shows three points \(A\), \(B\) and \(C\) on horizontal ground. \(A\) is at a bearing of \(040^\circ\) from \(B\) and \(C\) is at a bearing of \(125^\circ\) from \(A\). \(AB=60\text{ m}\) and \(AC=50\text{ m}\).

1. Find
   1. the bearing of \(B\) from \(A\),[1]
   2. the area of triangle \(ABC\),[2]
   3. the distance \(BC\),[2]
   4. angle \(ACB\),[2]
   5. the shortest distance \(AX\), where \(X\) is a point along \(BC\).[2]
2. Point \(A\) is the base of a vertical mast \(AT\). The angle of depression of \(C\) from \(T\) is \(33^\circ\). Find the greatest angle of elevation of \(T\) from a point along \(BC\).[3]