Draw a right triangle with a 30 degree angle
Let the side opposite the 30 degree angle be "1x".
Then by geometry we know the hypotenuse is "2x"
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
Then the tangent is opposite/adjacent =