Consider any sector of a circle of radius r whose arc length is L and whose area is A.
a. Prove that the ratio LA is equal to 2r, i.e. the ratio of the sector’s area to its arc length is always one-half of the radius, irrespective of the central angle.
b. A sector has radius 21 cm and area 277.2 cm2. Using the result of part (i), find the length of its arc. (Take π=722.)
c. Hence determine the central angle of this sector, correct to the nearest degree.