7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{c0993853-dd8f-4d14-aeed-b71ad60df09c-24_206_1040_356_443}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\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.
\begin{enumerate}[label=(\alph*)]
\item Find the tension in $A B$.
\item Find the tension in BC.
\item Find the value of $M$.\\

\begin{center}
\begin{tabular}{|l|l|}
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END &  \\
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\end{tabular}
\end{center}
\end{enumerate}

\hfill \mbox{\textit{Edexcel M1 2018 Q7 [12]}}