Features Extended:

Note that F_perpendicular = mgcos(θ) and F_parallel = mgsin(θ) are components of the gravitational force and NOT forces themselves. You should label components distinctly from forces to prevent confusion.
From Newton's 2nd law of motion (AKA F=ma), we find the acceleration of the object down the inclined plane is
```
  a = g[sin(θ)-μ_k*cos(θ)] 

        for sin(θ) > μ_s*cos(θ)
         or θ > θ_critical = arctan(μ_s) 
                           = μ_s*[1-(1/3)*μ_s**2 + ...]*(57.29577951 ... degrees)
                           ≅ 45*μ_s degrees

  a =   for θ ≤ θ_critical = as above , 
```
where we have used the arctangent infinite series and the conversion of radians to degrees (angle) (see Wikipedia: Radian: Conversion between radians and degrees; RapidTables: Radians to Degrees conversion calculator). The approximate equality is for an interpolation formula derived from the small-angle approximation to the arctangent plus an approximate conversion of radians to degrees (angle). The interpolation formula is exact for μ_s = 0 and μ_s = 1, and interpolates to better than 22 % error between μ_s = 0 and μ_s = 1 and has increasing error as μ_s grows above 1, but is under 20 % error to μ_s = 1.5
The results for acceleration "a" are independent of mass m which is a remarkable feature due to the canceling out of mass m everywhere.
Note that static friction coefficients for common materials are typically in the range 0.01--1 (see Wikipedia: Friction: Approximate coefficients of friction). Thus the interpolation formula for the critical angle θ_critical is usually at least fairly accurate.
By the by, the friction coefficients are considered dimensionless quantities. Why?
One meaning of dimension in physics is the basic nature of a quantity. For example, the basic nature of a force (i.e., any sort of force) is force (i.e., the thing that causes an acceleration relative to an inertial frame).
Now dimensionless, in fact, does NOT mean WITHOUT a basic nature. It just means (at least in the cases we'll consider) that the dimensionless quantity is the ratio of two quantities of the same basic nature. So the dimensionless quantity has the basic nature of the two quantities canceled out and it gives the relationship between the less-than-basic natures of the two quantities that does NOT cancel out.
In the case of the friction coefficients, the friction coefficients give the relationship between two kinds of force: the friction force and the normal force (which is partially the cause of the friction force).
If the two quantities in the ratio for the dimensionless quantity have the same units, the dimensionless quantity is usually considered to be in natural units which may or may NOT be given a name. For the friction coefficients, there is NO name for the natural units.
Another common dimensionless quantity is angle when considered as the ratio of an arc length along a circle to the radius of that circle. The natural unit in this case is given a name, the radian. The unnatural unit is the degree (°). Note 1 radian = (180°/π) = 57.29577951 ... degrees ≅ 60°.

File: Mechanics file: free_body_diagram_object_wedge_1bb.html .