Circular Curve of a Highway problem

1. The problem statement, all variables and given/known data
A circular curve of highway is designed for traffic moving at 95 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 110 m, what is the correct angle of banking of the road?


2. Relevant equations
F_y = N sin(theta) = (mv^2)/r
F_x = N cos(theta) = mg


3. The attempt at a solution

I assumed that if N = mg then I could cancel out m from either equation since I don't know it initially.
Then I would be left with:
sin(theta) = ((mv^2)/r)/N
cos(theta) = (mg)/N

I used my sin equation. With v = 26.38 m/s and r = 110 m and g = 9.8 m/s^2
I ended up with: sin(theta) = .64589 which is the coefficient of friction.
Doing the inverse sin of that equation, I got an angle of 40.23 degrees.
It was incorrect. What am I doing wrong?

 

There is no friction.

 

Sorry I thought LowlyPion replied to my question. I got an email with his response asking if there was friction or not.

Thanks for the hint! It worked!