11 Fig. 11.1 shows a village green which is bordered by 3 straight roads \(A B , B C\) and \(C A\). The road AC runs due North and the measurements shown are in metres.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b4c0b4b0-f13c-49a9-9f98-f86f28d1f577-4_460_1143_486_591}
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\caption{Fig. 11.1}
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- Calculate the bearing of B from C , giving your answer to the nearest \(0.1 ^ { \circ }\).
- Calculate the area of the village green.
The road AB is replaced by a new road, as shown in Fig. 11.2. The village green is extended up to the new road.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b4c0b4b0-f13c-49a9-9f98-f86f28d1f577-4_440_1002_1436_737}
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\caption{Fig. 11.2}
\end{figure}
The new road is an arc of a circle with centre O and radius 130 m . - (A) Show that angle AOB is 1.63 radians, correct to 3 significant figures.
(B) Show that the area of land added to the village green is \(5300 \mathrm {~m} ^ { 2 }\) correct to 2 significant figures.