The one real force is the force pulling toward the center of the earth — we calculate this by taking the product of mass, m, and g, the acceleration of gravity. F=mg.
This force is split into two component forces, one in the direction of travel down the inclined plane and the other force being the force going into the plane, the “normal force”.
We by using a right triangle. It should make sense at the component forces will be equal to or less than the actual Force. It should also make sense that if one of the component force is equal to the actual Force than the second component Force has to be zero.
The hypotenuse of the right triangle is the actual Force.
You can select any angle you want for the work we do to get the overall math, but we suggest picking an angle that is very shallow, like 20 degrees, so that most of the force will be going down into the plane and the force in the direction of travel will be much smaller.
Draw a right trangle, and designate the angle that is 20° to be Theta. We’ve already said that the small side represents the force in the direction of travel and noticed that the small side is the opposite side. We know that opposite / hypotenuse equals sine Theta.
Appendix A
We could have kept the same right triangle and made each side an acceleration. We would have had g for the actual acceleration, an acceleration in the direction of travel and an acceleration into the plane.
Appendix B
Our work focused on force in the direction of travel led to sine. Similar work focused on force into the plane would have led to cosine.
Rob Sterling 