InBrightestDay

So I’m working on Part Nine of The Woman in the Statue (the goal is to be done around the 18^th), and I wanted to describe the lobby of the Van Dijk building, but how big is it?

Now I could just bullshit this...but you all know I won’t.

So the building is about 300 meters tall and is a regular octagon in cross section (meaning all eight sides are the same length).  If the lobby in which Chloe, Luzurial and the assault team fight hybrids takes up one entire side (“edge” in geometric terms), how big across is it?

Well, if we assume the building has a base diameter of one sixth of its height, then it’s 50 m in diameter and thus has a circumradius (the radius of the circle connecting all eight vertices/corners of the octagon) of 25 m.  Each eighth of the octagon can be described as an isosceles triangle with two sides 25 m long (since those “sides” are the circumradius) meeting at an angle of 45 degrees.  So now I have to find the missing side.

Just to remind everyone that I am not a math major, I literally had to use Google to be reminded that an isosceles triangle is just two right triangles smooshed together, which I really should have remembered from 9^th Grade Geometry.  Anyway, since the sine (0.3826834323650897717284599840304) of one angle (22.5 degrees) of a right triangle is equal to the length of the opposite side divided by the length of the hypotenuse (25 m), and then we multiply that result (9.56708580912724429321149960076) by two to get the end of the isosceles…

So the lobby is about nineteen meters wide.  Why do I do this to myself?