Answer
$ 166.439 \ N; 113. 851 \ N$
Work Step by Step
The vertical components sum to $255$ N and can be given by $255 = a\cos 20^{\circ} +b \cos 30^{\circ} $
or, $0= a\sin 20^{\circ} -b \sin 30^{\circ} \implies a=\dfrac{b \sin 30^{\circ}}{a \sin 20^{\circ}} \implies 255 =\dfrac{b \sin 30^{\circ}}{ \sin 20^{\circ}} \cos 20^{\circ} +b \cos 30^{\circ}$
or, $255=b (\dfrac{\sin 30^{\circ}}{\sin 20^{\circ}} \cos 20^{\circ} +\cos 30^{\circ})$
or, $b \approx 113. 851 \ N$
and $a=\dfrac{b \sin 30^{\circ}}{ \sin 20^{\circ}} \approx \dfrac{(113.851) \sin 30^{\circ}}{\sin 20^{\circ}} \approx 166.439 \ N$
