The diameter of a circle is ___________the length of its radius?
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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
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.)
In the end you just have memorize the two tired triangles of trig.