2025 CCHY PRELIMS P2 Q7

The diagram shows a plot of land with points \(ABCD\) on level ground. The bearing of \(A\) from \(D\) is \(033^\circ\) and the length of \(AD\) is \(204\text{ m}\). \(B\) is \(50\text{ m}\) due east of \(A\). Angle \(ABC=142^\circ\) and the bearing of \(A\) from \(C\) is \(300^\circ\).

1. Find the bearing of \(C\) from \(A\).[1]
2. Find angle \(BAC\).[1]
3. Show that the distance \(AC\) is \(221.19\text{ m}\), correct to two decimal places.[2]
4. Find the area of triangle \(ABC\).[2]
5. Find angle \(DAC\).[1]
6. Hence, calculate the distance \(DC\).[3]
7. A tree, \(15\text{ m}\) tall, stands vertically at \(A\). Find the angle of elevation of the top of the tree from \(D\).[2]