Final answer:
To find the arc length for a 60° angle in a circle with a circumference of 6 units, you calculate (60°/360°) × 6, which equals 1 unit.
Step-by-step explanation:
The length of an arc in a circle can be calculated if we know the circumference of the circle and the angle that the arc subtends at the center, which in this case is 60°. Given that the circumference is 6 units, we first need to determine what fraction of the circle's circumference corresponds to a 60° arc. Since a full circle is 360°, a 60° arc represents ⅓ of the full rotation.
We know that the circumference (C) of a circle is given by the formula C = 2πr where r is the radius. For a full 360° revolution, the arc length is the same as the circumference, which is 2πr. Therefore, the arc length corresponding to a 60° angle would be ⅓ of the circumference.
Arc length for a 60° angle is therefore:
⅓ × 6 = 1 × 6 = 1 unit.