Banked Frictionless Curve, and Flat Curve with Friction

[Digitalx04]

Homework Statement

A car of mass M = 1200 kg traveling at 40.0 km/hour enters a banked turn covered with ice. The road is banked at an angle theta, and there is no friction between the road and the car's tires.

What is the radius r of the turn if \theta = 20.0 degrees (assuming the car continues in uniform circular motion around the turn)?

The Attempt at a Solution

I believe that F_{c} = F_{N} sin (\theta) = m(\frac{v^{2}}{r})

Using this I solved for r, which is my missing variable and came up with:

r = \frac{v^{2}}{F_{N}sin\theta}

Using this formula I get
r = \frac{11.1^{2}}{9.8 sin 20}

but when I submitted this answer it told me the normal force is not equal to the weight of the car.

My questions are what is the F_{N} value and am I missing another value in my equation?

 

[ideasrule]

Break down Fn into vertical and horizontal components. You already saw that the horizontal component provides the centripetal acceleration; what does the vertical component do?