A circle has a circumference of 18 cm. What is
the length of an arc that has a measure of 160°?

By definition, the length arc is a portion of a circle's circumference. The exact amount is directly proportional to the measure of the arc. Therefore, the formula for the length of an arc with measure (in degrees) [tex]\theta[/tex] is [tex]2\pi r\cdot \frac{\theta}{360}[/tex], where [tex]2\pi r[/tex] is the circumference of the circle.

Substituting [tex]2\pi r=18[/tex] and [tex]\theta=160^{\circ}[/tex]:

[tex]L_{arc}=18\cdot \frac{160}{360}=\boxed{8\:\mathrm{cm}}[/tex]

Okpalawalter8id Okpalawalter8id · Answer 2

We have that The length of an arc that has a measure of 160° is

[tex]l=7.9866cm[/tex]

From the Question we are told that

Circumference of 18 cm.

Arc angle=160

Generally the equation for length of arc is mathematically given as

[tex]l=2 \pi r (\theta /360)[/tex]

Where

[tex]C=2\pi r\\\\r=\frac{18}{2\pi}\\\\r=2.86cm[/tex]

Therefore

[tex]l=2 \pi 2.86 (160/360°)[/tex]

[tex]l=7.9866cm[/tex]

Therefore

The length of an arc that has a measure of 160° is

[tex]l=7.9866cm[/tex]

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