Answer
The weight of the crate is 64.8 lb
The tension in the horizontal rope is 61.9 lb
Work Step by Step
The weight of the crate is equal in magnitude to the vertical component of the tension in the first rope. We can find the weight of the crate:
$weight = (89.6~lb)~sin(46^{\circ}20')$
$weight = 64.8~lb$
The weight of the crate is 64.8 lb
The tension in the horizontal rope is equal in magnitude to the horizontal component of the tension in the first rope. We can find the tension in the horizontal rope:
$tension = (89.6~lb)~cos(46^{\circ}20')$
$tension = 61.9~lb$
The tension in the horizontal rope is 61.9 lb
