The figure shows a technique called rappelling, used by mountaineers for descending vertical rock faces. The climber sits in a rope seat, and the rope slides through a friction device attached to the seat. Suppose that the rock is perfectly smooth (i.e. there is no friction) and that the climber's feet push horizontally onto the rock. The climber's weight is 530 .
Find the tension in the rope/

It's impossible to answer exactly without seeing the figure to know what angle the rope is stretched at. However, bear in mind that if the climber is stationary (a.k.a. in equilibrium) then the sum of the horizontal components of all the forces, as well as the sum of the vertical components of all the forces, must equal zero.

The climber is being pulled downward by gravity with a force of 530g (where g is the acceleration of gravity, i.e. 9.8m/s^2, not the abbreviation for "grams"). Meanwhile, since the climber is in equilibrium, the vertical component of the force from the rope must be equal and opposite that of gravity. Since you know the total force applied by the rope is directed along it's length, and you presumably have been given the exact angle of the rope, you have enough information to solve for the remaining forces.

So just to reiterate, the climber is hanging from the rope, which is pulling upward and toward the cliff with some force T (which is equal to the tension in the rope). You don't know the value of T directly, but you know it's vertical component, and you also know the angle by which it deviates from perfectly vertical (let's call the angle ). Thus



Does that make sense to you?