Is this calculation correct? and why?

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1st - is my value correct

2nd - Why or why not?

I have a regular hexagon, which i know the height is 2 units and width is also 2 units. I am trying to find the value for one of the sides. I broke it down with triangles like so

hex image

now working with a 60,60,60 triangle, i know the Height of that triangle h = height/2 which would be 1

now i use Altitude of Equilateral Triangle h = (1/2) * √3 * a Not knowing what a (side)

with this i get that a is 1.1547, thus each side is 1.1547.

BUT..

If i use this next B B *--* * /| \ /| / | \ / | A*--*C * ==> c / | a \ / / | \ / / | *--* A*-----*C b a 30 , 60, 90 triangle, it is telling me c (side of hex) is 1.1547 (got from other calculation) and a would be sqt(3) which is 1.732... Which is not half of my height like i would think it should be. going by c = 2, b = 1 and a = sqrt(3)

So it makes me wonder what is the real way to find the side of a hex?

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At the same time you say "c (side of hex) is 1.1547 (got from other calculation)", and "c = 2". This can't work.