How to prove algebraic constructability of a 30 degree angle?

[Syrus]

Homework Statement

I don't know how to approach this proof, does this amount to proving that you can construct a line segment of length sin(30)?

Homework Equations

The Attempt at a Solution

 

[Curious3141]

Homework Statement

I don't know how to approach this proof, does this amount to proving that you can construct a line segment of length sin(30)?

Homework Equations

The Attempt at a Solution

Not sure what this question is asking for exactly, but if it's a matter of just showing you can construct the angle, the most obvious way is to construct an equilateral triangle and bisect the angle. Or construct the perpendicular bisector of one side and produce it to one of the vertices.

 

[DryRun]

Let each side of the equilateral be 2 units length. When you bisect the angle, you will get sin (30) = 1/2