斜面

More simply, an inclined plane is a ramp. You probably see inclined planes in your life. People on wheelchairs need inclined planes all the time so they are really important to understand. What we are interested in asking is $-$ what are the differences in the way forces behave on inclined planes and the way they behave on flat surfaces?

Indeed, gravity still points straight downwards. The reason a box might fall parallel to the incline plane and not plunge into the plane is because it is following the component of the force of gravity that is parallel to the plane, which brings us to our next topic $-$ normal force.

Similarly, if friction exists, it points up the plane and parallel to it.

Solution. Note that, after some trigonometry, the component of the weight parallel to the plane has magnitude $mg \sin \theta$. The only other force parallel to the plane is friction which has magnitude equal to $F_N \mu$, where $F_n$ is the normal force. By a similar logic as the component of weight parallel to the plane, we get that the component of weight perpendicular to the plane is of magnitude $mg \cos \theta$. Therefore, the force of friction has magnitude $mg \mu \cos \theta$.

We now set the force of friction and the parallel component of the weight equal to get $$mg \mu \cos \theta = mg \sin \theta \implies \mu = \tan \theta,$$ which is our answer.