A circle with circumference 18 has a central angle of 120 degrees what is the length of the arc?
Mathematics · College · Tue Nov 03 2020
Answered on
Given:
Circumference = 18
Central Angle = 120°
Find the arc length.
Arc length = (θ)( r )
Find first the value of r, in order to solve the arc length
Solution:
Solve for r in terms of the circumference.
C = 2πr
r = C/2π
r = 18/2π
r = 2.86
Next change the angle in degrees to radians. In order to do so, multiply the angle by π/180
=(120 degrees)(π/180)
= 2π/3
=2.0944 rad
Now the arc length can be solved. Substitute the value of theta and r in the given formula for the arc length.
Arc length = (θ)( r )
Arc length = (2.0944)( 2.86 )
Arc length = 6