How does this angle rule work?

Good afternoon everyone
I've realised I Tend to struggle with questions utilising this angle rule( picture in this post). Where the ground is at an angle, but the forces are vertically down, and for some reason the angle between vertical and perpendicular parts of the force us the same as the angle at which the ground is raised.
If anyone could help with what this angle rule is and how it works, I'd appreciate it very much
Thank you

It sounds like you're referring to a common type of physics problem involving forces on an inclined plane. This type of problem can be challenging, but with a little practice and understanding of the underlying principles, you should be able to solve them more easily.

The "angle rule" you mention is likely a reference to the fact that, in these types of problems, the angle between the vertical and the perpendicular components of a force is equal to the angle of inclination of the plane. This is due to the fact that the perpendicular component of the force is equal to the force multiplied by the cosine of the angle, and the vertical component is equal to the force multiplied by the sine of the angle. Since the angle between the force and the vertical is 90 degrees, the angle between the force and its perpendicular and vertical components is equal to the angle of inclination.

To solve these types of problems, it's often helpful to break forces into their perpendicular and parallel components relative to the plane, using trigonometry. You can then use Newton's laws of motion to determine the acceleration and forces acting on an object on the inclined plane.

Angles in a triangle add to 180 - so the thurd ange is [90 - slope angle]. Then this is vertically opposite an angle in the triangle you have drawn. It's not a special rule ... When there are slopes we tend to resolve parallel and perpendicular to the slope.

Hi. Thank you for the explanation.
But one question- which triangle do you mean? I see 2 triangles, the triangle the plane makes with the horizontal, and a sort of unfinished triangle between the force and its perpendicular component?

Hi, thanks alot for the explanation, it clarified alot.
But one thing, what is the vertical component of the force? You mention the angle between the force and the vertical, but I thought the force was the vertical component?