8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4f4eac7b-8908-480f-bb39-049944203fff-12_556_1392_210_283}
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\caption{Figure 2}
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Figure 2 shows the design for a triangular garden \(A B C\) where \(A B = 7 \mathrm {~m} , A C = 13 \mathrm {~m}\) and \(B C = 10 \mathrm {~m}\).
Given that angle \(B A C = \theta\) radians,
- show that, to 3 decimal places, \(\theta = 0.865\)
The point \(D\) lies on \(A C\) such that \(B D\) is an arc of the circle centre \(A\), radius 7 m .
The shaded region \(S\) is bounded by the arc \(B D\) and the lines \(B C\) and \(D C\). The shaded region \(S\) will be sown with grass seed, to make a lawned area.
Given that 50 g of grass seed are needed for each square metre of lawn, - find the amount of grass seed needed, giving your answer to the nearest 10 g .