How can I work out the width and height of a hexagon

Question

Each side is 60 degrees. and the top and bottom sides are horizontal

I think width = (cos(60) * sideLength * 2) + sideLength = sideLength * 2

This seems a bit off

Solution 1

width should be 2*sideLength (sideLength = cos(60) * sideLength * 2)

height will be sin(60) * sideLength * 2 = sqrt(3)*sideLength

Solution 2

I'm rubbish at maths so Wolfram Alpha is my go to site for any formula questions: http://www.wolframalpha.com/input/?i=diagonal+of+hexagon

and it agrees with @jswolf19: sqrt(3) * sideLength

Comments

[rubenvb]

+1 for Wolfram Alpha = math.stackexchange.com evolved into AI.

[Goz]

Actually if you check your link you'll see its 2 * sideLength ;)

[django11]

@Goz: no, it offers three formula for the three possible diagonals from each vertex: s | sqrt(3)s | 2s - from the OPs question: height would be sqrt(3)s and width 2s

[django11]

Umm, no... 2 * sin(30) = 1, so you're saying the height is the same as one sideLength!

[Goz]

Sorry ... I'm being a muppet :D

[Clifford]

@GrahamS: Good point ;) I read "Each side is 60 degrees." in the original and took that to mean the size of the internal angle, without second guessing it, but of course the size of the internal angle is 120 degrees. Duly modified, but @jswolf19 already gave that in any case.

[netpoetica]

Can you possibly update the formatting on this answer? I'm confused about that equal sine in front of cos(60) and also, I dont see how sin(6) * 5 * 2 = sqrt(3) * 5. It looks like you're trying to say there are two ways to do both, but both give different results.

[jswolf19]

@netpoetica, cos(60) = 1/2, sin(60) = sqrt(3)/2. Let me know if that doesn't clear it up, and I'll be a bit more verbose.