What is the magnitude of "F"

A block with a mass of 5.2kg is held in equilibrium on a frictionless incline of 33.0 degrees by the horizontal force F. The acceleration of gravity is 9.81m/s^2

What is the magnitude of F?
Answer in units of N.

What is the magnitude of the normal force?
Answer in units of N.

the component of gravity down the plane is mg sin(theta)

so the component of F up the plane must equal this

the component of F up the plane is F cos33, so we have

F cos 33 = mg sin 33 or F=mg sin33/cos 33 = mg tan 33 (sin/cos = tan)

substitute values and find F

there is no acceleration in the direction perpendicular to the plane, so we have:

N - component of weight perp to incline - component of F perp to incline =0

N - mg cos(theta) - F sin(theta) =0
N=mg cos(theta)+F sin(theta)

use values of m, g, theta and F to find N