Question

For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of

5
2
π meters?

Answer 1

arc length = (5/2) * PI meters = 7.853981634 meters
circle circumference = 2 * PI * radius = 2 *PI * 3
18.8495559215
arc length = (7.85381634 / 18.8495559215) * 360 =
0.4166578975 *360 =
150 degrees

Answer 2

`\boxed{\boxed{\theta=150^(\circ)}}`

Explanation:

We know that,

`\text{Arc length}=r\cdot \theta`

where,

r = radius,

θ = central angle in radian.

Given,

diameter = 6 m, so radius = 3 m.

`\text{Arc length}=(5)/(2)\pi`

Putting the values,

`\Rightarrow (5)/(2)\pi=3\theta`

`\Rightarrow \theta=(5)/(2* 3)\pi`

`\Rightarrow \theta=(5)/(6)\pi=(5)/(6)* 180^(\circ)=150^(\circ)`