From Förberedande kurs i matematik 1

We can work out the length we are looking for by taking the difference \displaystyle a-b\text{ } of the sides \displaystyle a and \displaystyle b in the triangles below:

If we take the tangent of the given angle in each triangle, we easily obtain \displaystyle a and \displaystyle b:

\displaystyle a=1\centerdot \tan 60^{\circ }=\frac{\sin 60^{\circ }}{\cos 60^{\circ }}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}