In a 3 phase "Wye" power set up, the voltage between phase A and B, for example is equal to the voltage of Phase A times the square root of 3.

Why the square root of 3?

 

Or Phase to star point voltage is phase to phase voltage /root3

 

Why the square root of 3?

Due to the 120° phase angle between the two phases.

 

sin(60) * 2 is equal to the square root of 3! I suppose it is futile to wonder why.

 

I suppose it is futile to wonder why.

Pythagoras.
Draw an equilateral triangle with a vertical line down the middle that splits it into two right angled triangles.
Hypotenuse is 1, adjacent is 0.5, so cosine is 0.5
opposite is therefore √(1-0.5^2) which, by a bit of algebra, =√(3/4) = √3/√4 = (√3)/2

 

RE: "Why the square root of 3"
Because sin(60 deg) is 0.5*sqrt(3)

 

Thank you !