2026 RSS P2 Q6

Triangle \(ABC\) is the boundary of a nature reserve.

\(A\), \(B\) and \(C\) are three points on level ground.

\(AB=7\) km.

\(C\) is \(12\) km due east of \(A\).

The area of the nature reserve is \(33\text{ km}^2\).

1. 1. Show that angle \(BAC=51.8^\circ\).[3]
   2. Calculate the length of \(BC\).[2]
   3. the bearing of \(B\) from \(C\).[3]
2. An observation deck is \(60\) m above point \(B\).
   1. A path is to be built from \(B\) to a point on \(AC\), across the nature reserve. Find the shortest possible length of the path.[2]
   2. A visitor is at the top of the observation tower. Find the greatest angle of depression from the top of the tower to a point on \(AC\).[2]