Conceptual Question about Static Friction

[TyroneTheDino]

Homework Statement

Today we were studying a block on an incline and determining the angle needed for the block to start sliding. The question asked is: Why is the equation for the coefficient of static friction independent of the weight of the block?

Homework Equations

ΣF_x=F_applied-f_s=0
ΣF_y=F_n-mgcosθ=0
μ_s=height/length

The Attempt at a Solution

My reasoning is that because the coefficient of static friction is reliant by height over length, weight has no involvement in this matter. If you double the weight of an object on an incline, the coefficient of static friction would still be proportional to coefficient if you were to leave the weight the same. I feel like I am on the right track, I just feel like my reasoning is missing proof.

 

[haruspex]

Why is the equation for the coefficient of static friction independent of the weight of the block?

That's strange wording. I would have expected a question like ""why is the coefficient of static friction independent of the weight of the block?"
Is it referring to the equation you quote, μ_s=height/length? That is not the definition of the coefficient of friction. (It's none of the equations you listed.) To answer the question properly, you need to reference the definition.