To Carry a 500-Pound Cylindrical Weight, Two Workers Lift on the Ends

To carry a 500-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder. One rope makes a $20 ^ { \circ }$ angle away from the vertical and the other makes a $30 ^ { \circ }$ angle as shown in the figure below. Find the vertical component of each worker's force. Round your answer to two decimal places.

A) $\| \mathbf { u } \| \sin 60 ^ { \circ } \approx 193.33 \mathrm { lb } ; \| \mathbf { v } \| \sin 110 ^ { \circ } \approx 306.67 \mathrm { lb }$
B) $\| \mathbf { u } \| \sin 60 ^ { \circ } \approx 242.33 \mathrm { lb } ; \| \mathrm { v } \| \sin 110 ^ { \circ } \approx 355.67 \mathrm { lb }$
C) $\| \mathbf { u } \| \sin 60 ^ { \circ } \approx 203.33 \mathrm { lb } ; \| \mathbf { v } \| \sin 110 ^ { \circ } \approx 316.67 \mathrm { lb }$
D) $\| \mathbf { u } \| \sin 60 ^ { \circ } \approx 354.33 \mathrm { lb } ; \| \mathbf { v } \| \sin 110 ^ { \circ } \approx 467.67 \mathrm { lb }$
E) $\| \mathbf { u } \| \sin 60 ^ { \circ } \approx 387.66 \mathrm { lb } ; \| \mathbf { v } \| \sin 110 ^ { \circ } \approx 614.34 \mathrm { lb }$