Question

Find the length of arc EG. Round to the nearest hundredth.(degrees)

Answer 1

step 1

Find out the circumference of circle F

`C=2\pi r`

we have

r=EF=16 units

substitute

`\begin{gathered} C=2\pi(16) \\ C=32\pi\text{ units} \end{gathered}`

step 2

Remember that the circumference of a circle subtends a central angle of 360 degrees

so

Applying proportion

Find out the length of arc EG using a central angle of 122 degrees

`(32\pi)/(360^o)=(x)/(122^o)`

Solve for x

x=32pi*122/360

using a calculator for pi

x=34.07 units

therefore

the length of arc EG is 34.07 units