Find the Central Angle

Question

Find the central angle of a circle whose radius is 5ft and the arc length is 14.84ft.

Answer 1

Start with the arc length formula:

s = rθ where

1. s is arc length
2. r is radius
3. θ is central angle in radians

Get θ by itself by dividing both sides by r

θ = s/r

Plug in known values for s and r

θ = 14.84ft/5ft

Perform the division

θ = 2.968 radians

If you need the angle in degrees instead of radians, multiply the angle in radians by 360°/2π

θ = 2.968 radians * 360°/2π

θ = 170.05°

Answer 2

m∠θ = 14.84 / 5 radians