Question

A crate of weight W is being pushed across a horizontal surface by a force directed at an angle of 20 below the horizontal. What is the magnitude of the normal force on the crate

Answer 1

Assuming there's no friction, we have a net vertical force acting on the crate of

∑ F[vertical] = n - W + f sin(-20°) = 0

where n = magnitude of normal force and f = magnitude of applied force. It follows that

n - W - f sin(20°) = 0

n = W + f sin(20°)

and there's not much more to say without any additional information.