OCR MEI C2 (Core Mathematics 2)

2 Fig. 10.1 shows Jean's back garden. This is a quadrilateral ABCD with dimensions as shown. \begin{figure}[h] \end{figure}

1. (A) Calculate AC and angle ACB . Hence calculate AD .
   (B) Calculate the area of the garden.
2. The shape of the fence panels used in the garden is shown in Fig. 10.2. EH is the arc of a sector of a circle with centre at the midpoint, M , of side FG , and sector angle 1.1 radians, as shown. \(\mathrm { FG } = 1.8 \mathrm {~m}\). \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cd507fa5-97b2-4edd-ae37-a58aea1de5ed-2_579_981_1512_567} \captionsetup{labelformat=empty} \caption{Fig. 10.2}
   \end{figure} Calculate the area of one of these fence panels.

3 \begin{figure}[h] \end{figure} \section*{Not to scale} In Fig. 3, BCD is a straight line. \(\mathrm { AC } = 9.8 \mathrm {~cm} , \mathrm { BC } = 7.3 \mathrm {~cm}\) and \(\mathrm { CD } = 6.4 \mathrm {~cm}\); angle \(\mathrm { ACD } = 53.4 ^ { \circ }\).

1. Calculate the length AD .
2. Calculate the area of triangle ABC .

4

1. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cd507fa5-97b2-4edd-ae37-a58aea1de5ed-4_492_1018_256_567} \captionsetup{labelformat=empty} \caption{Fig. 10.1}
   \end{figure} At a certain time, ship S is 5.2 km from lighthouse L on a bearing of \(048 ^ { \circ }\). At the same time, ship T is 6.3 km from L on a bearing of \(105 ^ { \circ }\), as shown in Fig. 10.1. For these positions, calculate
   (A) the distance between ships S and T ,
   (B) the bearing of S from T .
2. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{cd507fa5-97b2-4edd-ae37-a58aea1de5ed-4_430_698_1350_573} \captionsetup{labelformat=empty} \caption{Fig. 10.2}
   \end{figure} Not to scale Ship S then travels at \(24 \mathrm {~km} \mathrm {~h} { } ^ { 1 }\) anticlockwise along the arc of a circle, keeping 5.2 km from the lighthouse L, as shown in Fig. 10.2. Find, in radians, the angle \(\theta\) that the line LS has turned through in 26 minutes.
   Hence find, in degrees, the bearing of ship S from the lighthouse at this time.

5 Fig. 7 shows a sketch of a village green ABC which is bounded by three straight roads. \(\mathrm { AB } = 92 \mathrm {~m}\), \(\mathrm { BC } = 75 \mathrm {~m}\) and \(\mathrm { AC } = 105 \mathrm {~m}\). Fig. 7 Calculate the area of the village green.

6
Not to scale \begin{figure}[h] \end{figure} Fig. 7 shows triangle ABC , with \(\mathrm { AB } = 8.4 \mathrm {~cm}\). D is a point on AC such that angle \(\mathrm { ADB } = 79 ^ { \circ }\), \(\mathrm { BD } = 5.6 \mathrm {~cm}\) and \(\mathrm { CD } = 7.8 \mathrm {~cm}\). Calculate

1. angle BAD ,
2. the length BC .