2 A wooden frame is to be made to support some garden decking. The frame is to be in the shape of a sector of a circle. The sector \(O A B\) is shown in the diagram, with a wooden plank \(A C\) added to the frame for strength. \(O A\) makes an angle of \(\theta\) with \(O B\).
\includegraphics[max width=\textwidth, alt={}, center]{be9ad375-d3cd-488c-9e3b-a4cd035d0d1d-02_419_627_1695_847}
2
- Show that the exact value of \(\sin \theta\) is \(\frac { 4 \sqrt { 14 } } { 15 }\)
[0pt]
[3 marks]
2 - Write down the value of \(\theta\) in radians to 3 significant figures.
2 - Find the area of the garden that will be covered by the decking.