An arc 33m long subtends a central angle of a circle with a radius of 16m. Determine the measure of the central angle in radians

Answer 1

To determine the measure of the central angle in radians, we first need to find the circumference of the circle using the formula:

Circumference = 2 * π * radius

Substitute the radius value (16m) into the formula:

Circumference = 2 * π * 16
Circumference = 32π

Since the arc length is 33m, and it subtends a central angle of the circle, we can set up a proportion to find the central angle in radians:

(Length of arc) / (Circumference) = (Central angle) / (2π)

Substitute the given values:

33 / 32π = θ / 2π

Multiplying both sides by 2π to isolate θ:

θ = 2π * (33 / 32π)
θ = 2 * (33 / 32)
θ = 66 / 32
θ ≈ 2.0625 radians

Therefore, the measure of the central angle in radians is approximately 2.0625 radians.