Start with a simple cartesian grid. Draw a circle, and call this the unit circle.
You know that in a unit circle, the radius is always 1. You also know that sin(A) = opp/hyp. hyp is thus always 1, and the y coordinate of a point on the unit circle is the perpendicular distance from the x-axis to the point, so it can represent the "opp" side. It is always less than 1. So, you can estimate, by eye, the y value of the point, and this is the value of the sine of the angle.
If you make the circle big enough, and divide the x and y axis into a hundred or so points between the origin and the maximum values of the circle, you can read off the value of sin(20) or any other angle with reasonable accuracy. The more points you can get along the axes, the better your precision.
You know that in a unit circle, the radius is always 1. You also know that sin(A) = opp/hyp. hyp is thus always 1, and the y coordinate of a point on the unit circle is the perpendicular distance from the x-axis to the point, so it can represent the "opp" side. It is always less than 1. So, you can estimate, by eye, the y value of the point, and this is the value of the sine of the angle.
If you make the circle big enough, and divide the x and y axis into a hundred or so points between the origin and the maximum values of the circle, you can read off the value of sin(20) or any other angle with reasonable accuracy. The more points you can get along the axes, the better your precision.