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