Embarrassing trigonometry problem

[FreshDK]

Hi Guys,

There maybe a specific forum for math problems somewhere, but I figure there must be enough brain power in here to solve this rather embarrassing case for me.

I actually got a engineering degree and consider myself skilled in the mathematical world, but 10 years of project management work is staring to leave its marks :D I spend more hours on this already that I would care to admit.

So, I got a circle with a known diameter. Inside that circle there is a smaller 6-sided polygon with same center as the circle. I need a equation to determinate the side length of the 6-sided polygon as a function of the circle diameter and "perpendicular corner offset" between the circle diameter and the 6-sided polygon.

I need S as a function of h and r referring to below (poor) illustration. Any who can solve this?

 

[FreshDK]

Thank you so much for all the effort!! I should have posted that I cracked the obviously simple equation last night before I went to bed.

It really is simple once you draw the correct aid lines.

Have a look at this sketch:

 

[BSALV]

with radius R=1

h= -.998 * S + 1.0216 or h= -.1402 * S^2 -.85818 * S +.999
driehoeken

I didn't see you solved it already this morning,
Normally, that formula of mine should have trigometric fomulas inside

	-0,99838​	1,021588​	-0,99838​
-0,1402​	-0,85818​	0,999389​	0,999998​

 

[Anthony47]

Thank you so much for all the effort!! I should have posted that I cracked the obviously simple equation last night before I went to bed.
It really is simple once you draw the correct aid lines.
Have a look at this sketch:

I am curious to know which formula was developed on that sketck

Have a nice day

 

[BSALV]

with 2 sides (S en R) and 1 angle (150°) known, that triangle is known, but not documented here.

 

[Anthony47]

Oh yes, I see; with two known sides and one angle either trigonometry or analytic geometry will give you the answer.
(btw in the problem the known terms are R and H)

Thank you