We can relate the length of the diagonal D with the length of the sides of a regular octagon a with the formula:
[tex]D=a\sqrt[]{4+2\sqrt[]{2}}[/tex]We know that D = 15, so we can find a as:
[tex]\begin{gathered} D=15 \\ a\sqrt[]{4+2\sqrt[]{2}}=15 \\ a=\frac{15}{\sqrt[]{4+2\sqrt[]{2}}} \\ a\approx\frac{15}{\sqrt[]{4+2.8284}} \\ a\approx\frac{15}{\sqrt[]{6.8284}} \\ a\approx\frac{15}{2.6131} \\ a\approx5.74 \end{gathered}[/tex]NOTE: I did all the calculations without approximating, but as we have irrational numbers, it is always an approximated result.
Answer: the side length is approximately 5.74 meters long.
