How do you determine the radian measure of a central angle in a circle with a radius of 80 kilometers that intercepts an arc length of 160 kilometers?

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Calculating the Radian Measure of a Central Angle

To find the radian measure of the central angle that intercepts a given arc length in a circle, we can use the formula:

θ = s / r

  • θ is the central angle in radians.
  • s is the length of the arc.
  • r is the radius of the circle.

In this scenario, we have:

  • Radius r = 80 kilometers
  • Arc length s = 160 kilometers

Now, substituting the known values into the formula:

θ = 160 km / 80 km

Doing the calculation:

θ = 2 radians

Thus, the radian measure of the central angle that intercepts an arc length of 160 kilometers in a circle with a radius of 80 kilometers is 2 radians.

Understanding this relationship is essential in various fields such as physics, engineering, and even computer graphics, where circular paths and rotations are common.

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