Question indigenous Dave, a parent:

I would prefer to know at what length and angle ns would reduced wood to make a Hexadecagon.

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Hi Dave,

A hexadecagon is a 16 sided polygon. Ns have likewise seen it dubbed a hexadecagon or a hexakaidecagon. Ns assume you typical a consistent hexadecagon, one whereby all the sides room the exact same length and also all the inner angles are equal in size. If you join each vertex of a regular hexadecagon come the center you partition the figure into 16 congruent triangles. Three of them are in mine diagram below and also one is labeled as triangle ABC. I also let w be the width of the hexadecagon.


Since the 16 triangles are congruent angle BCA = 360o/16 = 22.5o. Because the triangle abc is isosceles angles ABC and also CAB room congruent. Hence angle alphabet = (180o - 22.5o)/2 = 78.75o and angle ABD = 2 × 78.75o = 157.5o.

The size s you reduced each side, for example s = |AB|, depends on how huge you want the hexadecagon to be. Look in ~ triangle alphabet again.


If p is the midpoint of abdominal then |PB| = s/2, |CP| = w/2 and angle BCP = 22.5o/2 = 11.25o. Hence

tan(11.25o) = |PB|/|CP| = s/w

and thus

s = 0.1989 w

I expect this helps,Penny

In December that 2013 we received this question keep in mind Felly

I have read the write-up above, but I don"t understand just how the .1989 number is calculated. I would like to employ the very same math for a 20 sided polygon, the tangent being 9 degrees instead that 11.25, so ns assume the multiplier would adjust accordingly? Thx!

Hi Felly,

In a ideal angled triangle such as triangle $BPC$ over if you choose one that the non-right angles, such as angle $BCP$ climate the tangent the this edge is the size of opposing side divided by the length of the surrounding side. For this reason in the example above

< anleft(BCP ight) = frac>


< anleft(11.25^o ight) = fracsw>

and thus

What stays is to uncover the worth of $ anleft(11.25^o ight).$ because that this I used my calculator. I input 11.25 and then pressed the switch labeled tan. Mine calculator reverted 0.1989...

You need to take care that her calculator is in degree mode. To make certain calculate $ anleft(11.25^o ight).$ If you acquire 0.1989 then you have the right to proceed through your angle. If friend don"t get 0.1989 her calculator is most likely in radian mode and you have to switch that to level mode.

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Write earlier if friend need much more assistance, Penny

Math main is supported by the college of Regina and The Pacific Institute because that the mathematical Sciences.