Determine sine alpha, where alpha is the angle of a regular dodecagon

From the school geometry course, we know that the inner angle of a regular polygon can be calculated using the following formula:

a = (n – 2) / n * 180.

Let us determine what value the inner corner of the polygon will correspond to when it is known from the condition of our problem that it has 12 sides:

(12 – 2) / 12 * 180 = 10 * 15 = 150.

As we know, sin (90 ° + a) will be equal to cos a, therefore:

sin 150 ° = sin (90 ° + 60 °) = cos 60 °.

cos 60 ° = 1/2.

Answer: Under these conditions sin a = 1/2.