Question 36126
find the exact value of tan 30 degrees

Draw a right triangle with a 30 degree angle
 Let the side opposite the 30 degree angle be "1".
Then by geometry we know the hypotenuse is "2" 
because " the side opposite the 30 degree angle is 
one-half the hypotenuse".
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
Cheers,
Stan H.