Question

In circle F with m \angle EFG= 122m∠EFG=122 and EF=16EF=16 units, find the length of arc EG. Round to the nearest hundredth.

Answer 1

Given:

In circle F, $m\angle EFG=122^\circ,\ EF=16$ units.

To find:

The length of arc EG.

Solution:

It is given that, $m\angle EFG=122^\circ,\ EF=16$ 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:

$s=2\pi r\times \dfrac{\theta}{360^\circ }$

Where, r is the radius and $\theta$ is the central angle in degrees.

Putting $r=16,\ \theta=122^\circ,\ \pi=3.14$, we get

$s=2(3.14)(16)\times \dfrac{122^\circ}{360^\circ }$

$s=100.48\times \dfrac{61}{180}$

$s=34.0515556$

$s\approx 34.05$

Therefore, the length of arc EG is 34.05 units.