How would you find the apothem of a regular polygon when given the length of a side, or vise versa.

I've been running into problems where I have to solve this out, and I'm a bit confused.
Any help would be appreciated.

Question

How would you find the apothem of a regular polygon when given the length of a side, or vise versa.

I've been running into problems where I have to solve this out, and I'm a bit confused. 
Any help would be appreciated.

rational · Answer

familiar with SOH-CAH-TOA ?

anonymous · Answer

I kind of understand them.
Sine-opposite/hypotenuse, cosine=adjacent/hypotenuse, tan=Opposite/adjacent. 
But I don't exactly understand how to use them.

rational · Answer

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rational · Answer

can you find that angle intercepted by the side ?

anonymous · Answer

I think.  So would it be 5/6(tan-1)?
If so then it would be 39.805...

rational · Answer

the angle doesn't depend on the length of side

rational · Answer

Notice that it has 8 sides, so the angle is simply $\large \dfrac{360}{8} = 45$

anonymous · Answer

Alright, so the angle depends on the sides. 
So what would I need to find next?

rational · Answer

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