What is for 2015?

Angles Ratio = 2:3:7

So $2x+3x+7x=180$ and the angles are $30,45,105$

Smallest side is always opposite to smallest angle so

Use $a,b,c$ sides and $A,B,C$ Angles $\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}=2R$ side_length=2015 units

Solving for Circumradius R $\frac{2015}{sin30}=2R$ Circumradius $\boxed{R=2015}$ units

The sum of angles in a triangle is 180.

So, 2k+3k+7k = 180 which implies that 12k = 180 and k=15 degrees.

So, the angles are 30,45 and 105 degrees.

The shortest side is opposite to the shortest angle.

R(circumradius) = abc/4(Area). where a is the shortest side.

Where a,b, and c are side lengths.

Area is also equal to $\frac { 1 }{ 2 } bcsinA$ .

So, R = $\frac { abc }{ 4\frac { 1 }{ 2 } bcsinA } =\frac { a }{ 2sinA }$ which is popularly known as the sine rule.

Now, R = 2015/1 = 2015 which is the circumradius of the triangle.

Given

The angles of a triangle are in the ratio 2:3:7

$\Rightarrow$ 2x+3x+7x=180

$\Rightarrow$ x=5

Therefore the angles are 30,45,105

We know that

$\frac {a}{\sin A}$ = $\frac {b}{\sin B}$ = $\frac {c}{\sin C}$ =2R

In the above equation, a,b,c are sides of the triangle , R is circumradius

Since given the smallest side is 2015.Therefore the angle opposite to the side 2015 is 30

$\frac {2015}{\sin 30}$ =2R

$\Rightarrow$ R=2015

Therefore the circumradius of the triangle is 2015