2025 CGS PRELIMS P2 Q5

\(A\), \(B\) and \(C\) are points on the horizontal ground. \(B\) is at a bearing of \(290^\circ\) and \(800\text{ m}\) away from \(A\). \(C\) is due north of \(A\) and at a bearing of \(60^\circ\) from \(B\).

1. Find \(BC\).[2]
2. Show that \(AC\) is approximately \(707.64\text{ m}\).[2]
3. \(CT\) is a vertical tower at \(C\). When Betty is at \(A\), the angle of elevation of the top of the tower, \(T\), is \(20^\circ\). Find \(CT\).[2]
4. Find the largest angle of elevation of \(T\) as Betty walks from \(A\) to \(B\).[3]