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

$\frac{32\pi}{360^o}=\frac{x}{122^o}$

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