Jeremy S. answered • 6d

Experienced Physics and Math Tutor

Let's go through what you did on this problem.

Tension in cable T_{BD}: 500lbs ← Yes! The cable must lift the box against gravity. Your reasoning that tension in the cable must balance the weight of the box is correct here.

One adjustment on your equations: Cables AB and BC are pulling in opposite horizontal directions. This means that the x-component of T_{BC} is the negative of the x-component of T_{AB}. This gets you

T_{BC}*(5/13) + T_{AB}sin(50˚) = 500

T_{BC}*(12/13) - T_{AB}cos(50˚) = 0

It looks like that is your only issue, and you should be able to solve this problem from there.