Question

Circle D has a radius of 21 millimeters and central angle, ∠EDF, which measures 60°. Find the exact length of Arc of EF .

Answer 1

central angle = 60
radius = 21mm

Length of Arc = ∅/180 × radius

EF = (60/360) x (21) = 7 mm

Answer 2

`7 \pi\ mm`

Explanation:

we know that

The circumference of a circle is equal to

`C=2\pi r`

In this problem we have

`r=21\ mm`

substitute

`C=2\pi (21)=42\pi\ mm`

`360\°` subtends the complete circle of length equal to
`42\pi\ mm`

so by proportion

Find the length of arc which a central angle of
`60\°`

`(42\pi)/(360)(\ mm)/(degrees)=(x)/(60)(\ mm)/(degrees) \\ \\x=42\pi *60/360\\ \\ x= 7 \pi\ mm`