The circle has radius 6 feet, so its total circumference is 2π • (6 ft) = 12π ft.
As an arc, the complete circle corresponds to a central angle of 2π radians. So the red arc corresponds to a central angle θ such that
θ / (15 ft) = (2π rad) / (12π ft)
Then
θ = (15 ft) • (2π rad) / (12π ft) = 15/6 rad = 2.5 rad
