Please! Don't break out in hives just yet. In today's era of technology, there are ways to avoid radicals. The picture below illustrates my problem. How long is the red line (the point at which it crosses the square made of dots?
What if you cannot find an applet or slick Internet thingie?
Well, you could just look at it and guess. I plotted three numbers: 10, 11, and 12. It looks like it's half way between 11 and 12. You may not get credit for it being right on an exam, but it works in real life.
How can I know for sure? In the 30º-60º-90º standard right triangle, one side is exactly twice the other, but which one? Sometimes, math only requires looking and thinking. The short side seems half of the longest (the hypotenuse). That means the short leg is half of 11.5, or 5.75. The sides of our triangle are about 5.75, 10, and 11.5.
Now, if we apply Pythagoras (a² + b² = c²), the results are a little off. However, 11.5 is good enough for curve stitching.