10 At 1200 the captain of a ship observes that the bearing of a lighthouse is \(340 ^ { \circ }\). His position is at A.
At 1230 he takes another bearing of the lighthouse and finds it to be \(030 ^ { \circ }\). During this time the ship moves on a constant course of \(280 ^ { \circ }\) to the point B .
His plot on the chart is as shown in Fig. 11 below.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{73d1c02b-1b7b-426d-a171-c762597cfed4-3_501_1156_661_387}
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\caption{Fig. 11}
\end{figure}
- Write down the size of the angles LAB and LBA .
- The captain believes that at A he is 5 km from L . Assuming that LA is exactly 5 km , show that LB is 4.61 km , correct to 2 decimal places, and find AB . Hence calculate the speed of the ship.
- The speed of the ship is actually 10 kilometres per hour. Given that the bearings of \(340 ^ { \circ }\) and \(030 ^ { \circ }\) and the ship's course of \(280 ^ { \circ }\) are all accurate, calculate the true value of the distance LA.