Radius of circumference circumscribed to a triangle

[greg_rack]

Homework Statement

Find the radius of circumference circumscribed to an equilateral triangle of side=8cm

Relevant Equations

No equations needed

At first I had no idea of how to solve this problem, but checking online I found out that there is a formula linking the radius of the circumference and the side of the triangle... the formula is:
side=radius√3
The thing is that I can't understand why is this working... which deduction have been made to derive it?

 

[Lnewqban]

Check this out:
https://www.mathopenref.com/trianglecircumcircle.html

The law of sines establishes a common ratio for all the lengths of the sides of a triangle to the sines of its angles.
That ratio is the diameter (2 x radius) of the unique circle in which that triangle can be inscribed (circumscribed circle of the triangle).

Copied from
https://en.m.wikipedia.org/wiki/Circumscribed_circle#Other_properties

“The diameter of the circumcircle, called the circumdiameter and equal to twice the circumradius, can be computed as the length of any side of the triangle divided by the sine of the opposite angle:

As a consequence of the law of sines, it does not matter which side and opposite angle are taken: the result will be the same.”