## Problem 1108

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.*