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 = \frac{s}{r}. Substitute the values for s and r.

θ = \frac{s}{r}

=\frac{53}{51}

\approx 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.

 

 

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