In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.
The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.
Rounded to the nearest hundredth, this is approximately 10.68 units.