Question

A hexagon is inscribed in a circle As see in the picture.Find the length of an arc between consecutive vertices. Round to the nearest hundred

Need help homework

Answer 1

Answer:

The length of the arc between consecutive vertices is:

$S=8.38\: in$

Step-by-step explanation:

The angle between consecutive vertices is 60°, it is because it forms an equilateral triangle.

Now, the length arc is defined as:

$S=R\theta$

Where:

• R is the radius (R = 8 in)
• θ is the angle of the arc

We see the angle is in grades, but we need to convert it to radians.

$\theta=\frac{60^{\circ}}{360^{\circ}}(2\pi)$

$\theta=1.05\: rad$

Finally, the length of the arc between consecutive vertices will be:

$S=8*1.05$

$S=8.38\: in$  

I hope it helps you!