Answer:
[tex]\theta= cos^{-1}(\frac {N}{mg})[/tex]
Explanation:
From the attached sketch where the box represents a car travelling up a hill. The normal force of the car [tex]N=mgcos \theta[/tex] where m is the mass of the car and g is the gravitational constant
This can be re-written as [tex]cos\theta= \frac {N}{mg}[/tex]
Getting the inverse of [tex]cos\theta[/tex] we have [tex]\theta= cos^{-1}(\frac {N}{mg})[/tex]
From the diagram also, the ratio of normal force to weight is [tex]cos\theta[/tex]
[tex]\frac {mg cos\theta}{mg}=cos\theta[/tex]
Conclusively, [tex]\theta= cos^{-1}(\frac {N}{mg})[/tex]
