Question

The sector AOB is described by ∡AOB and the radius of circle O. Find the length of arc AB. Leave answers in terms of π.

If ∡AOB= 240° and r= 12, then the arc length is

Answer 1

Answer:

The length of an arc depends on the radius of a circle and the central angle θ. We know that for the angle equal to 360 degrees (2π), the arc length is equal to circumference. Hence, as the proportion between angle and arc length is constant, we can say that:

L / θ = C / 2π

As circumference C = 2πr,

L / θ = 2πr / 2πL / θ = r

We find out the arc length formula when multiplying this equation by θ:

L = r * θ

Hence, the arc length is equal to radius multiplied by the central angle (in radians).