Answer
the weight is $30.1$ $\bf{N}$
the mass is $\frac{30.1}{9.8}$ $\approx$ $3.07$ $kg$
Work Step by Step
The forces acting on the chain then are the tension vectors $\bf{T_1}$, $\bf{T_2}$ in each end of the chain and the weight $\bf{w}$, as shown in the figure.
We know $|$$\bf{T_1}$$|$ $=$ $|$ $\bf{T_2}$$|$ $=$ $25$ N
in terms of vertical and horizontal components, we have,
$\bf{T_1}$ $=$$−25$$cos$$37$$^{\circ}$ $\bf{i}$ $+$ $25$$sin$$37$$^{\circ}$ $\bf{j}$
$\bf{T_2}$ $=$$25$$cos$$37$$^{\circ}$ $\bf{i}$ $+$ $25$$sin$$37$$^{\circ}$ $\bf{j}$
$\bf{T_1}$ $+$ $\bf{T_2}$ $=$ $\bf{-w}$
$\bf{w}$ $=$ $\bf{-|w|}$ $\bf{j}$
$−25$$cos$$37$$^{\circ}$ $\bf{i}$ $+$ $25$$sin$$37$$^{\circ}$ $\bf{j}$ $+$ $25$$cos$$37$$^{\circ}$ $\bf{i}$ $+$ $25$$sin$$37$$^{\circ}$ $\bf{j}$ $=$ $\bf{|w|}$ $\bf{j}$
$50$$sin$$37$$^{\circ}$ $\bf{j}$ $=$ $\bf{|w|}$ $\bf{j}$
$\bf{|w|}$ $=$ $50$$sin$$37$$^{\circ}$ $\approx$ $30.1$
So the weight is $30.1$ $\bf{N}$
since $w$ $=$ $mg$
then the mass is $\frac{30.1}{9.8}$ $\approx$ $3.07$ $kg$
