2025 MGS(S) PRELIMS P1 Q24

\(A\), \(B\) and \(C\) are points on level ground. Angle \(ABC=130^\circ\). \(A\) is \(75\text{ m}\) from \(B\) on a bearing of \(210^\circ\). \(B\) is \(110\text{ m}\) from \(C\) on a bearing of \(260^\circ\).

1. Calculate the distance \(AC\).[2]
2. Calculate the bearing of \(C\) from \(A\).[3]
3. A kite is flying \(55\text{ m}\) vertically above \(B\). Find the greatest angle of elevation of the kite observed by a person walking in a straight path from \(A\) to \(C\).[4]