2025 Nov TZ3 P2 Q2

A boat sets off from a port P and travels on a bearing of \(090^{\circ}\) until reaching point B.
A lighthouse L is \(5\) km from P on a bearing of \(056^{\circ}\).
The bearing of the lighthouse from B is \(290^{\circ}\).
This is shown in the following diagram.

1. Find the angle \(\mathrm{L\hat{P}B}\).

   [1]

2. Find \(\mathrm{LB}\), the distance from point \(\mathrm{L}\) to point \(\mathrm{B}\).

   [4]