the sector length is 50cm and the angle is 120degrees, what is the radius?

Question

please provide calculation/formulae with your answer. thank you

Answer 1

The sector length s=rx, where x is measured in radians. 1 degree is (pi)/180 radians, so 120 degrees is 120(pi)/180 radians=2(pi)/3. So 50=2(pi)r/3 making r=3*50/(2(pi))=75/(pi)=75/3.1416=23.87cm approx.

Another way of solving this is s/(2(pi)r)=120/360=1/3 (length of sector divided by the circumference of the circle is the same fraction as the angle of the sector divided by 360). So 50/(2(pi)r)=1/3 or r=75/(pi).