Problem

6.

A washing line $ABCD$ 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 $3\,\mathrm{kg}$ and the item at $C$ is modelled as a particle of mass $M\,\mathrm{kg}$.

The section $AB$ makes an angle $\alpha$ with the horizontal, where $\tan\alpha=\frac34$, the section $BC$ is horizontal and the section $CD$ makes an angle $\beta$ with the horizontal, where $\tan\beta=\frac{12}{5}$, as shown in Figure 3.

The system is in equilibrium.

(a) Find the tension in $AB$.

(b) Find the tension in $BC$.

(c) Find the value of $M$.