Question

Find the circumradius if 2 is the side of the triangle with the opposite angle $\frac{\pi}{3}$.

Answer 1

To find the circumradius of a triangle, we can use the formula:
R = $\frac{a}{2sin(A)}$
Where R is the circumradius, a is the length of a side of the triangle, and A is the opposite angle.
In this case, we have the side length a = 2 and the opposite angle A = $\frac{\pi}{3}$. Substituting these values into the formula, we get:
R = $\frac{2}{2sin(\frac{\pi}{3})}$
Now, we can simplify the expression:
R = $\frac{2}{(2\times\frac{\sqrt{}3}{2})}$
R =$\frac{2}{(\sqrt3)}$
R = $\frac{2\sqrt3}{3}$
Therefore, the circumradius of the triangle is $\frac{2\sqrt3}{3}$.