A box of mass 2.75 kg sits on a table. Neglect friction. You pull on a string tied to the right side of the box, exerting a force of 20.0 N at an angle of 35.0 degrees above the horizontal. Your friend exerts a horizontal force of 12.0 N by pulling on a string on the other side of the box.
(a) What is the box's acceleration?
(b) What is the normal force exerted on the box by the table?
Draw the freebody diagram  show all the forces acting on the box.
Think about what the box will do.
The force of gravity is mg = 2.75 x 9.8 = 26.95 N, directed down. The vertical component of your force is less than that, so the box remains on the table. If it accelerates it will accelerate horizontally.
Choose a coordinate system.
Assume the box accelerates to the right, so +x = right and +y = up.
Apply Newton's second law twice, once for the xdirection and once for the ydirection.
In the x direction, summing the forces gives:
Σ F_{x} = m a_{x}
T_{1} cos(35)  T_{2} = m a_{x}
a_{x}  = 

= 

=  1.6 m/s^{2} 
The fact that it's positive means the box does accelerate to the right.
In the y direction, there is no acceleration, which means the forces have to balance.
Σ F_{y} = m a_{y} = 0
N + T_{1} sin(35)  mg = 0
N = mg  T_{1} sin(35)
N = 26.95  11.47 = 15.5 N
Note that in this case the normal force is not equal in magnitude to the force of gravity.