Now your seeing what I can't relate to, what do you mean by the ratio?
Think of the
gear ratios in your bike:
For 4[SUP]th[/SUP] gear (and I'm making this up) lets say the
gear ratio is 4 to 1, in other words, for one, single rotation of the crankshaft, 4[SUP]th[/SUP] gear transfers
4 rotations to the rear axle.
Another way to state that ratio is by the fraction 4/1 (read it as 4 to 1), or 4, or 400% (all these can be done on the calculator).
At the other end, for 1[SUP]st[/SUP] gear, with a ratio of 1 to 4, it would be the exact opposite (4 rotations of the crank shaft to 1 rotation of the wheel), or a ratio of 1/4, or 0.25, or 25%.
For right triangles, sin(q) = opposite / hypotenuse, or the sine is the ratio of length of the opposite (vertical) leg divided by the length of the hypotenuse (the sloping part).
That "ratio" number (as a decimal) can be converted to an angle between the two lines that composed of the bottom line of the triangle and the hypotenuse, at the point where they meet.
Think I've got this right...
<EDIT> Another thought: A ratio is used to express a
difference between two items that are
related (gears in a transmission, lines and angles that make up a triangle, people who vote for or against an issue). If there are
no difference(s), the ratio is
1; any difference at all and the ratio is either more, or less, than 1.