3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ee5f81bc-1bdb-47a1-81e7-7e3cb8219e91-06_618_803_244_630}
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\caption{Figure 1}
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The uniform lamina \(A B D E\) is in the shape of a rectangle with \(A B = 8 a\) and \(B D = 6 a\). The triangle \(B C D\) is isosceles and has base \(6 a\) and perpendicular height \(6 a\). The template \(A B C D E\), shown shaded in Figure 1, is formed by removing the triangular lamina \(B C D\) from the lamina \(A B D E\).
- Show that the centre of mass of the template is \(\frac { 14 } { 5 } a\) from \(A E\).
The template is freely suspended from \(A\) and hangs in equilibrium with \(A B\) at an angle of \(\theta ^ { \circ }\) to the downward vertical.
- Find the value of \(\theta\), giving your answer to the nearest whole number.