2026 NCHS P2 Q7

The diagram shows a rectangular box, \(ABCDEFGH\).

The box has a length of 60 cm and breadth of 24 cm.

The angle of elevation of \(A\) from \(G\) is \(54.32^\circ\).

A rectangular card \(HIJK\) is placed against edge \(DH\) and face \(ABFE\) of the box as shown.

The top edge of the card is 11 cm below the top of the box. The edge, \(HNI\), of the card is perpendicular to the diagonal, \(EG\), of the base of the box.

1. Find \(AE\).[2]
2. Show that \(EN=8.91\text{ cm}\), correct to 2 decimal places.[3]
3. By showing your calculations clearly, determine if point \(G\) can be seen by a person looking straight from point \(A\).[2]