It's all about the relationship between the hypotenuse of a right triangle and one of the adjacent sides. On a sine bar (or sine plate) the two points of contact on the bottom, generally cylindrical pins sometimes called rolls, are a very closely controlled distance apart and represent a line that is the hypotenuse of the triangle. Generally, sine plates and bars are available in either a 5 or 10" distance between the rolls. One roll is set on the reference surface, and the other is elevated (or if used horizontally, rotated) a fixed distance according the the sin*5 (or 10) for the given angle. Note that the base side of the generated right triangle is of no real consequence here. It's probably easiest to understand if you think on the terms of setting this up on a surface plate. One end (sometimes if not most often) has a small plate attached to it to keep any work inclined to not slide off. So if you set the "fixed" roll on the plate, and want to create a 30° inline on the sine bar, calculate the sine value for 30° (which happens to be 0.5000) and multiply it by the distance between the rolls (5 or 10), and then we know what elevation we need to get the inclined angle to be 30°. So in our example, we have 5.000 inches, multiplied by 0.5000 and get 2.5000. Stack up gage blocks, or set an adjustable parallel to that and elevate the other roll, and the top of the bar will be exactly 30°.
You can use this concept in many ways, limited only by your imagination. You can set up work with it, as well as inspect work with it.