Find the radian measure of the central angle of a circle of radius 80 kilometers that intercepts an arc length of 160 kilometers?

Solution:

Given a radius of 80km and an arc length is 160 km

We know that the arc length can be defined as the product of radius and central angle

Arc length = radius × central angle

L= r × θ

160 km = 80 km × θ

θ = 160/80

θ = 2°

We know that 1 Degree × (π/180) = 0.01745 rad

2 degrees × (π/180) = 0.01745 rad × 2 = 0.035 radians

θ = 0.035 radians

The radian measure of the central angle of 0.035

Find the radian measure of the central angle of a circle of radius 80 kilometers that intercepts an arc length of 160 kilometers?

Summary:

The radian measure of the central angle of a circle of radius 80 kilometers that intercepts an arc length of 160 kilometers is 0.035