4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f7a2bf93-a7fc-43c5-b317-109320f633ba-05_783_1231_237_358}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A set square \(S\) is made by removing a circle of centre \(O\) and radius 3 cm from a triangular piece of wood. The piece of wood is modelled as a uniform triangular lamina \(A B C\), with \(\angle A B C = 90 ^ { \circ } , A B = 12 \mathrm {~cm}\) and \(B C = 21 \mathrm {~cm}\). The point \(O\) is 5 cm from \(A B\) and 5 cm from \(B C\), as shown in Figure 1.
- Find the distance of the centre of mass of \(S\) from
- \(A B\),
- \(B C\).
The set square is freely suspended from \(C\) and hangs in equilibrium.
- Find, to the nearest degree, the angle between \(C B\) and the vertical.