The "radius of the triangle"? Do you mean that the triangle is inscribed in a circle of radius 1? If so, then since 120= 360/3, you have an equilateral triangle. Let x be the length of the chord (one side of the triangle) and let r be the radius of the circle. Dropping a perpendicular to one side from the opposite angle divides the triangle into two right triangle having hypotenuse of length x and one leg of length x/2. By the Pythagorean theorem, the other leg, an altitude of the triangle, has length .

Now draw a line from the center of the circle to one of the other two vertices of the triangle. That, together with the altitude just drawn, gives a right triangle with hypotenuse r (the radius of the circle) and one leg of length x/2. The other leg, along the altitude, again by the Pythagorean theorem, has length . But that altitude is that leg plus a radius: so that .

Squaring both sides, . Now the " " terms cancel giving . Dividing both sides by x, .

Now take r= 1 and r= 3438 to answer your questions.