2025 SJI PRELIMS P2 Q7

A field \(ABCD\) on horizontal ground is crossed by path \(BD\). \(D\) is due east of \(A\), \(AD=200\text{ m}\), \(BC=48\text{ m}\), angle \(ABD=95^\circ\), and the bearing of \(B\) from \(A\) is \(045.8^\circ\).

1. Calculate \(BD\).[2]
2. The area of triangle \(BCD\) is \(3300\text{ m}^2\). Calculate the bearing of \(C\) from \(B\).[3]
3. A vertical tower of height \(80\text{ m}\) stands at \(C\). Sally walks from \(B\) to \(D\) and reaches \(P\), where the angle of elevation of the tower top is greatest. Find this angle.[4]