A circle with an arc measure of 160 degrees has an arc length of LaTeX: 20\pi\:cm20 π c m What is the radius of the circle in which the arc sits? Round to the nearest tenth if necessary.

the radius of the circle is 22.5 cm

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Length of arc = 20π cm

θ = 160 degrees

Therefore,

20π = 160/360 × 2 × π × r

20π = 160/360 × 2 × π × r

Dividing both sides of the equation by π, it becomes

20 = 160/360 × 2r

20 × 360 = 160 × 2r = 320r

320r = 7200

r = 7200/320

r = 22.5 cm