Question

Given a side length of 18 inches, find the height of a stop sign rounded to the rearest tenth.

Answer 1

Stop sign is a Regular Octagon.
External Angles are 360º/8 = 45º
Internal Angles are 180º - 45º = 135º

Consider one side, with radii drawn from the center. This creates a 67.5º-67.5º-45º isosceles triangle.

Consider the apothem (aka Hieght of the isosceles triangle). \(\tan(67.5º) = \dfrac{Height}{½\cdot 18"}\)

Now what?

Note: There are likely easier ways. This is just the first thing that popped to mind.