5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6a5d0ffc-a725-404b-842a-f3b6000e6fed-14_470_940_246_500}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows the plan view of a viewing platform at a tourist site.
The shape of the viewing platform consists of a sector \(A B C O A\) of a circle, centre \(O\), joined to a triangle \(A O D\).
Given that
- \(O A = O C = 6 \mathrm {~m}\)
- \(A D = 14 \mathrm {~m}\)
- angle \(A D C = 0.43\) radians
- angle \(A O D\) is an obtuse angle
- \(O C D\) is a straight line
find
- the size of angle \(A O D\), in radians, to 3 decimal places,
- the length of arc \(A B C\), in metres, to one decimal place,
- the total area of the viewing platform, in \(\mathrm { m } ^ { 2 }\), to one decimal place.