Find the central angle 
which subtends an arc of length 53 miles of a circle of radius 51 miles.
Solution:-
A center angle is a angle whose vertex is at the center. The rays of a central angle subtend (intersect) an arc on the circle. The arc length for a circle of radius r and a central angle of radians is given by s = r.
Solving this expression for given = 
. Substitute the values for s and r.
=
= 
(Substitute s = 53 and r = 51.)
1.039.
Therefore, the central angle which subtends an arc of length 53 miles of a circle of radius 51 miles is = 1.039 radians.