Banked Curve

1. The problem statement, all variables and given/known data
A curve with a 140m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction between tires and road needed to prevent skidding?

2. Relevant equations
F_fr = MkN
N = mgcosθ
∑F = ma
∑F_net-x = mv^2/r = Nsinθ

3. The attempt at a solution
I have drawn my xy coordinate system so that the x component is parallel to the curve, and , and found that the normal force is mgcosθ. However, I don’t know how to combine my equations together to find an angle theta. Is finding an angle here even the proper approach if the problem does not ask for it? Should I be doing something else instead?

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