In a 30- 60 - 90 right triangle, let the side opposite the 30° angle = 1

Then the side opposite the 90° will be twice as long = 2

Then the side opposite the 60° angle = sqrt (2^2 - 1^2 } = sqrt (3)

So the tangent of 60° = opposite side / adjacent side = sqt(3) / 1 = sqrt (3)