Two cables hold a mass of 100kg, joining in the middle of the top of the mass. Two helicopters lift a cable each and hover so that the height of the mass is constant. Each cable makes an angle of 57° with the normal. Find the tension in each cable.

Once you note that the height is constant, the key thing to remember here is that there is no unbalanced force acting on the mass. By this, I mean that since the mass is not accelerating (it is actually at rest, just hovering) adding up all of the forces acting on the mass should equal to 0.
Free body diagrams (diagrams showing the forces acting on something) tremendously help with this type of problem. Drawing a free body diagram of the mass will show that there are three forces acting on the mass. The two identical tensions pointing in the direction of the cable at the top of the mass each at 57° to the normal, and the weight of the mass pointing directly downwards. Since the mass is hovering at rest, the total force downwards (the weight) must equal the total force upwards (the vertical components of the tensions).
This is simple if you think about it. The weight is just W=mg=980N. There are two cables sharing the weight equally, so each cable must have a vertical component of 980/2=490N. Now we can use trigonometry to find the tension.
The vertical component is adjacent to the angle with the normal, and the tension is the hypotenuse of the angle with the normal. So we must use cos(57°)=adjacent/hypotenuse or rather cos(57)=a/h, rearrange for h to give:
h=a/cos(57)=490/cos(57)=900N
So the tension T=900N.