Consider a block resting on a plane that is slowly tilted. Two forces act along the incline: the gravity component W sin θ pulling the block down the slope, and the friction force resisting it. Friction can rise only up to a maximum value, the limiting friction = μN = μ W cos θ, where μ is the coefficient of static friction.

As the angle θ increases, W sin θ grows while the maximum available friction μ W cos θ falls. At one particular angle they become equal and the block is just on the verge of sliding:

• W sin θ = μ W cos θ
• ⇒ tan θ = μ

This critical angle, whose tangent equals the coefficient of friction, is called the angle of friction (for loose granular material the same idea is called the angle of repose). It is the maximum inclination the surface can have before the body begins to slide, so it is the correct answer.

Static friction is the force that resists motion before sliding, not an angle. Limiting friction is the maximum value of that static friction force, again a force and not an angle. Cone angle belongs to the geometry of cone clutches/pulleys and is unrelated to sliding on an incline. Only the angle of friction correctly names the limiting inclination.