7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c0993853-dd8f-4d14-aeed-b71ad60df09c-24_206_1040_356_443}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A washing line \(A B C D\) is fixed at the points \(A\) and \(D\). There are two heavy items of clothing hanging on the washing line, one fixed at \(B\) and the other fixed at \(C\). The washing line is modelled as a light inextensible string, the item at \(B\) is modelled as a particle of mass 3 kg and the item at \(C\) is modelled as a particle of mass \(M \mathrm {~kg}\). The section \(A B\) makes an angle \(\alpha\) with the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\), the section \(B C\) is horizontal and the section \(C D\) makes an angle \(\beta\) with the horizontal, where \(\tan \beta = \frac { 12 } { 5 }\), as shown in Figure 2. The system is in equilibrium.
- Find the tension in \(A B\).
- Find the tension in BC.
- Find the value of \(M\).