Question

what is the arc length of a circle that has an 8 inch radius and a central angle that is 95° is 3.4 for pie and round your answer to the nearest hundredth

Answer 1

Explanation:

if angle \theta is in radians,then

\theta=l/r

where l= arc length

r=radius of circle.

`\theta=(l)/(r)\\or\\l=r \theta\\180^\circ=\pi ~radians\\95^\circ=(\pi * 95)/(180)`

`l=8 * (95 \pi)/(180) =(760 \pi)/(180)=(76 \pi)/(18)=(38 \pi)/(9)`

`l\approx(38 * 3.14)/(9)\approx 13.26~in`

if π=3.4

`l=(38 * 3.4)/(9)\approx 14.36~in`