I am not sure I understand but let me try. My understanding is that you have an octagon as in the diagram below, you can measure the distance s and you want to calculate the distance r.
If my understanding of the problem is correct then you can proceed as follows.
If you join each vertex to the center C of the octagon then you divide the octagon into 8 congruent triangles.
The measure of the angle ACB is then 130/8 = 45o. Draw a line from C to the midpoint M of the line segment BA then ACM is a right triangle, the length of AM is s/2 and the measure of angle ACM is 45/2 = 22.5o.
Using trigonometry sin(ACM) = |AM|/|AC|. But sin(ACM) = sin(22.5o) = 0.3827 and
|AC| = r, thus
r = |AM|/0.3827 = s/(2 * 0.3827) = s/0.7654 = 1.307 s.