How do calculators calculate Sin Cos and Tan of an angle without side lengths?

The relationship between an angle and the triangle formed by it is always constant. This is also why sin cos and tan obtained from the unit circle can be applied to all triangles with the same angle. All that matters is the ratio of the sides, so the calculator can "pick" any length for one side, and use that and the angle to find the other side(s). This answer will be the same regardless of which triangle you are specifically referring to. Side lengths 3 and 5 will produce the same trig values as sides 21 and 35. Also, given the processing power of most calculators, these values are often programmed in, similar to how many students are "programmed" to know the trig values for major angles such as pi, pi/4, 30deg, and 60deg.