how is this dimensionally correct?

why does the degrees or if expressed in radians,disappear i.e. why does length of an arc have unit meters and not radian meter/ degree meter? Can someone explain it with other units?
how is this dimensionally correct?

why does the degrees or if expressed in radians,disappear i.e. why does length of an arc have unit meters and not radian meter/ degree meter? Can someone explain it with other units?