Step 1: Draw a special right triangle with a 60° angle.

            NOTE: A special right triangle 30\degree-60\degree-90\degree.                                    

                  It's sides are 1, 2 and \sqrt{3}

Step 2: Recall the definition of tangent and calculate \tan\ 60\degree

            DEFINITION: The tangent (tan) of an angle in a right triangle is a ratio.

                                  It is the length of the opposite side(opp) divided by the

                                    length of adjacent side (adj).

            NOTE:  The length of the opposite is \sqrt{3}

                         The length of the adjacent  side is  1             

                          \tan60\degree=\frac{opp}{adj}=\frac{\sqrt{3}}{1}

                                 and

Step 3: Calculate \tan\ 30\degree

                 The length of the opposite side is  1

                   length of the adjacent side is \sqrt{3}

                   \tan30\degree=\ \frac{opp}{adj}

                    \tan30\degree=\frac{1}{\sqrt{3}}