Final answer:
The length of each side of an equilateral triangle with one vertex at (0,3) and rotational symmetry about the origin is 3 units.
Step-by-step explanation:
The question asks to determine the length of each side of an equilateral triangle with a vertex at (0,3) and rotational symmetry about the origin. To solve this problem, we must recognize that in such a triangle, all sides are equal in length and all angles are 60 degrees. Since the triangle has rotational symmetry about the origin, and one vertex is at (0,3), the triangle must be positioned such that the other two vertices are at equal distances from the origin and form 120-degree angles to the first vertex. As the vertex is 3 units above the origin, and all angles in the triangle are equal, the triangle is rotated around the origin in such a manner that each side is horizontal at some rotation. As this is an equilateral triangle with sides of equal length, the length from the origin to each vertex is the same, which is also the altitude of the triangle. This length is 3 units; therefore, the length of each side of the triangle is 3 units as well.