Trigonometry as taught is mostly about memorizing two lousy triangles, namely half a square and half an equilateral triangle. This one is half an equilateral triangle.
The respective opposite sides of the 30/60/90 triangle are in ratio [tex]1:\sqrt{3}:2[/tex]
A sine of √3/2 is an opposite of √3 and a hypotenuse of 2, so opposite and hypotenuse of the 60 degree angle. (It's the mama bear, in the middle, just right.)
[tex]\sin 60^\circ = \dfrac{\sqrt{3}}{2}[/tex]
In the end you just have memorize the two tired triangles of trig.
