Because the ratios of the sides of right triangles can be used in many useful ways, we have named them. The ratio, expressed as a decimal fraction, of the length of the side opposite an angle, divided by the length of the hypotenuse (the longest side of a right triangle) is called the sine of the the angle.
Before scientific calculators, we used printed trig. (trigonometry) tables to determine what the sine of a particular angle was. Now all we have to do is enter the angle in a scientific calculator and push the "sin" button.
Once we have the sine of a particular angle, we can use what we do know to calculate what we do not.
Since we do know that your sine bar, that takes the position of the hypotenuse in a right triangle ( a triangle that has a 90 degree angle) is 6", we can say that X (the number that we are solving the equation for) divided by 6 equals the sine of the angle.
There are 60 minutes in a degree; 20 minutes may be expressed as a third of a degree, or .33 degree (rounded).
Going back to our scientific calculator and entering .33 and hitting the sin key gives us the sine of the angle as .0058 (rounded).
If we then multiply both sides of the equation by 6, we get x on one side and six times .0058 on the other. six times .0058 equals .0348, which rounds to .035.
I wish that I could use a white board to explain this. It is harder to understand as a narrative.