Question

A circle has a radius of 17 cm find the length s of the arc intercepted by a central angle of 66 degrees

Answer 1

Circumference = 2*17 pi = 34pi cms

length of s = (66/360) * 34 pi = 6.233 pi = 19.58 cm to nearest hundredth

Answer 2

Arc length (s) = radius (r) x θ (in radians)

First, convert 66° into radians using the proportion π = 180°

`( \pi)/(180) = (x)/(66)`

`(66 \pi )/(180) = x`

`(11 \pi )/(30) = x`

s = r θ
= 17 (
`(11 \pi )/(30)`)
=
`(187 \pi )/(30)`

Answer:
`(187 \pi )/(30)` ≈ 19.6 cm