Suppose in the diagram above, the person was pushing down at a $30$ angle with $200N$ of force. The desk still does not move.

a$.$ Draw a free$-$body diagram for the desk.

b$.$ Write the equation that describes the forces that act in the $x-$direction.

c$.$ Write the equation that describes the forces that act in the $y-$direction.

d$.$ Determine the value of the frictional force. Do the same for the normal force.