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

Answer:

$\boxed{\boxed{\theta=150^{\circ}}}$

Step-by-step 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.

$\text{Arc length}=\dfrac{5}{2}\pi$

Putting the values,

$\Rightarrow \dfrac{5}{2}\pi=3\theta$

$\Rightarrow \theta=\dfrac{5}{2\times 3}\pi$

$\Rightarrow \theta=\dfrac{5}{6}\pi=\dfrac{5}{6}\times 180^{\circ}=150^{\circ}$

Answer 2

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