Final Answer:
Three 60°-sectors of a unit circle form a semicircle (180°), which corresponds to half the perimeter of an equilateral triangle inscribed in the circle. Thus, the correct answer is option C. 3π.
Step-by-step explanation:
The side length of the equilateral triangle can be determined by considering the relationship between the central angles of the unit circle and the corresponding arcs formed by the sectors inside the triangle. Each sector has a central angle of 60 degrees, covering 1/6th of the unit circle. Three such sectors combine to form a semicircle (180 degrees), which corresponds to half the perimeter of the equilateral triangle.
Since the full perimeter of the equilateral triangle is made up of two semicircles, the side length of the triangle is given by the formula: Side length = 2 * Radius * π.
For a unit circle, the radius is 1, so the side length of the equilateral triangle is 2 * 1 * π = 2π. However, the question asks for the side length of the triangle, not the perimeter. Therefore, the correct answer is half of the calculated value, which is 3π.
Thus, the correct answer is option C. 3π.