Answers

2016-03-11T15:13:46+08:00
Tangent = opposite / adjacent
in a right triangle having 30°, the adjacent side is √3 and the opposite side is 1.
so opposite / adjacent = 1/√3 or √3 / 3.

I don't know if this is what you wanted to know.
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2016-03-11T20:38:40+08:00
Exact tangent of 30° 
Using Pythagoras you can find the 2rd side, as follows:
1^2 + x^2 = 2^2
x^2=3
x=sqrt 3
Then the tangent is opposite/adjacent = 1/sqrt3 = sqrt3/3
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