Step 1 :Given the equation of a circle: \((x+3)^2 + (y-7)^2 = 289\)
Step 2 :The radius squared is 289, so the radius is \(\sqrt{289}\)
Step 3 :Calculate the square root of 289: \(\sqrt{289} = 17\)
Step 4 :\(\boxed{17}\) is the radius of the circle.