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.