Given:
In circle F, [tex]m\angle EFG=122^\circ,\ EF=16[/tex] units.
To find:
The length of arc EG.
Solution:
It is given that, [tex]m\angle EFG=122^\circ,\ EF=16[/tex] units. It means the central angle of arc EG is 122 degrees and the radius of the circle F is 16 units.
Formula for arc length is:
[tex]s=2\pi r\times \dfrac{\theta}{360^\circ }[/tex]
Where, r is the radius and [tex]\theta [/tex] is the central angle in degrees.
Putting [tex]r=16,\ \theta=122^\circ,\ \pi=3.14[/tex], we get
[tex]s=2(3.14)(16)\times \dfrac{122^\circ}{360^\circ }[/tex]
[tex]s=100.48\times \dfrac{61}{180}[/tex]
[tex]s=34.0515556[/tex]
[tex]s\approx 34.05[/tex]
Therefore, the length of arc EG is 34.05 units.
