Side Lengths of the Unit Triangles
Since the Unit Circle has radius=1 unit, the special right triangles that exist in the Unit Circle all have a hypotenuse=1 unit.
We can determine the side lengths of each unit triangle. Each square root expression has been converted to decimal form for your reference. Notice the labeled side lengths on each triangle. The applet also shows calculated side length ratios within each triangle. Click "Unitize" to make the hypotenuse equal to 1 (as it would be in the Unit Circle) Unitize each of the triangles to determine the side length values used in the Unit Circle.