An object is in equilibrium under four concurrent forces in the directions shown in figure. Find the magnitudes of ${\mathbf{F}}_1$ and ${\mathbf{F}}_2$.

The object is in equilibrium. Hence,

$\Sigma F_x=0$

$\therefore 8+4\cos 60°-F_2\cos 30°=0$

or

$8+2-F_2\frac{\sqrt{3}}{2}=0$

$F_2=\frac{20}{\sqrt{3}}N$

$\Sigma F_y=0$

$\therefore F_1+4\sin 60°-F_2\sin 30°=0$

or

$F_1+\frac{4\sqrt{3}}{2}-\frac{F_2}{2}=0$

or

$F_1=\frac{F_2}{2}-2\sqrt{3}=\frac{10}{\sqrt{3}}-2\sqrt{3}$

or

$F_1=\frac{4}{\sqrt{3}}N$