Question

In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?

Answer 1

Explanation:

Answer: 1/3 if the circumference of Circle L

Why:

this is because the measure of the arc, 120 degrees, is equivalent to its length. since arc MNOP is 120 units in length and the circumference length is 360, 120 is 1/3 if 360 (120/360 = 1/3)

Answer 2

The length of arc is 10.46 units

Explanation:

Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of the ray after rotation is called the terminal side of the angle. The point of rotation is called the vertex.

If the direction of rotation is called anticlockwise, the angle is said to be positive

And if the direction of rotation is called clockwise, then angle is said to be negative

see the diagram (1)

Radian measure:-

Angle subtended at the center by an arc of length '1' unit it is a unit circle(circle of radius 1 unit) is said to have a measure of one radian.

see diagram (2)

By using formula
`r =(l)/(theta)`

here 'r' be the radius and θ be the angle measure and 'l' be the length of arc

l = r θ

given radius r= 5

given angle θ = 120 =
`(2\pi )/(3)`

l = 5 X
`(2\pi )/(3)` =
`(10\pi )/(3)`

The length of arc is 10.46 units