CPM Homework Help : PC3 Problem 8-121

Rectangle labeled 100 pounds, 2 rays start at center of top edge, left, labeled 30 pounds, goes up & left, & makes 30 degree angle with top of rectangle, right, labeled 75 pounds, goes up & right, & makes 50 degree angle with top of rectangle. Two forces are being used to lift a $100$ pound box as shown in the diagram below. Can they lift the box? Use vector operations to justify your answer.

Hint:

There are two forces pulling up on the box, but there is also the force of the box pulling straight down.
Compute the resultant force. Is it in a positive or negative vertical direction?

Step:

$\langle 30\cos\left(30^{\large \circ }\right), 30\sin\left(30^{\large \circ }\right)\rangle+\langle75\cos\left(50^{\large \circ }\right), 75\sin\left(50^{\large \circ }\right)\rangle+\langle0,-100\rangle$