1 Fig. 11.1 shows a village green which is bordered by 3 straight roads \(\mathrm { AB } , \mathrm { BC }\) and CA . The road AC runs due North and the measurements shown are in metres.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{139b1905-2035-4503-9ffb-3e6e81f78ef9-1_459_1141_424_629}
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\caption{Fig. 11.1}
\end{figure}
- 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 \(A B\) 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]{139b1905-2035-4503-9ffb-3e6e81f78ef9-1_432_574_1377_779}
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\caption{Not to scale}
\end{figure}
Fig. 11.2
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.
Fig. 4
For triangle ABC shown in Fig. 4, calculate - the length of BC ,
Not to scale
- the area of triangle ABC .