Question

A box is held at rest by two ropes that form 30° angles with the vertical. The tension T in either rope is 42 N. What is the weight (w) of the box?

Answer 1

So I'm picturing the ropes as both tied to the same point on the top of
the box, and forming a " V " as they leave it, with each side of the 'V'
tilted 30° away from the vertical. It really doesn't matter whether they're
tied to the same point or to different points. Everything is in equilibrium,
nothing is moving, we don't have to worry about the horizontal components
of the tension, and all we have to find is the vertical components.

The vertical component of tension in each rope is 42 cos(30°).

There are 2 ropes, so the net upward force on the box is

84 cos(30°) = 72.75 newtons (rounded)

Everything is in equilibrium, nothing is accelerating, so the net
upward force on the box is equal to its weight.