3.
\begin{figure}[h]
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\caption{Fig. 1}
\end{figure}
Figure 1 shows a uniform triangular lamina \(A B C\) placed with edge \(B C\) along the line of greatest slope of a plane inclined at an angle \(\theta\) to the horizontal. The lengths \(A C\) and \(B C\) are 15 cm and 9 cm respectively and \(\angle A B C\) is a right angle.
- Find the distance of the centre of mass of the lamina from
- \(\quad A B\),
- \(B C\).
Assuming that the plane is rough enough to prevent the lamina from slipping,
- find in degrees, correct to 1 decimal place, the maximum value of \(\theta\) for which the lamina remains in equilibrium.
(4 marks)