Find the radian measure of the central angle of a circle of radius r = 90 inches that intercepts an arc of length s = 130 inches.

Solution:

The statement of the problem given above is summarized in the figure below:

θ = s/r

s = rθ

where s = arc length

r = radius of the circle

θ = angle the measure of which is in radians

θ = 130/90 = 1.44 radians

Find the radian measure of the central angle of a circle of radius r = 90 inches that intercepts an arc of length s = 130 inches.

Summary:

The radian measure of the central angle of a circle of radius r = 90 inches that intercepts an arc of length s = 130 inches is θ = 1.44 radians