2025 DSS PRELIMS P1 Q23

The diagram shows the position of an island \(A\) at sea level. Boat \(B\) and ship \(C\) are on the surface of the sea. Ship \(C\) lies due east of island \(A\). Angle \(BAC=38^\circ\).

1. Calculate the bearing of \(A\) from \(B\).[2]
2. On the diagram above, construct a line such that every point on this line is equidistant from the lines \(AB\) and \(AC\). The line intersects \(BC\) at \(P\). Measure the length \(BP\).[2]