A box is dragged along the floor. The rope that is acting on the box makes an angle A to the floor. How much force is being used to drag the box ?

In the rope occurs a tension that is dragging the box and
tends to lift the box. If the angle made by the rope to the floor is smaller, the force
that is dragging the box will be greater. If the rope is parallel to the floor, the
lifting component won't exist, at all.

The component of the
tension that dragging the box is the horizontal
component.

F horiz. = F*cos
a

If the tension in the rope is 300 N and the angle made by
the rope to the floor is 30 degrees, the horizontal component
is:

F horiz. = 300 N*cos 30

F
horiz. = 300*sqrt3/2

F horiz. = 150sqrt3
N

The vertical component of the tension, the
lifting force is:

F vert =
300N*sin30

F vert =
150N

Now, we must take in consideration the
friction that brakes the box when it is dragged on the
floor.

The friction is opposite to the horizontal component
of the tension from the rope, when the object is moving at constant
speed.

Friction = - F
horiz.

Friction = -150sqrt3
N