1. A smooth bead $B$ of mass $m$ grams is threaded on a light, inextensible string.
The ends of the string are fixed at two points $A$ and $C$, with $A$ vertically above $C.$

The section $AB$ of the string makes an angle of 35° with the vertical.

The section $BC$ of the string makes an angle of 55° with the vertical.

The bead is held in equilibrium by a horizontal force of 3 N acting towards the left, as shown in Figure 1.

The only forces on the bead are its weight and the tensions in $AB$ and $BC$.

Taking $g$ = 9.8 ms^-2, find the value of $m$.