(a) This can be found by calculating the horizontal component of the force applied and then dividing that by the mass of the box. As you may have noticed, horizontal components usually are found by using cos. it's no different here.
Now that we have Fhor we divide it by the mass of the box to get acceleration:
(b) The normal force, as we recall, is equal and opposite of the force of gravity. Fg=mg; m is the mass of the box and g is the acceleration due to gravity so we have:
So since FN=-Fg we have that FN=-274.9N.
But we also need to take into account the veritcal component of the pull on the box (this force counteracts FN). To do that we find the vertical component through the Soa part of SoaCahToa:
Now we just add Fver and FN to get the real FN.