Answer:
The measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°
Step-by-step explanation:
Here, the diameter of the circle = 6 m
Diameter = 2 x RADIUS
So, radius = D / 2 = 6 / 2 = 3 m
Also, the length of the arc = ( [tex]\frac{5}{2} \pi[/tex]) meters
Putting π = 3.14, we get
The length S of the arc = [tex]\frac{5}{2} \times (3.14) = 7.85[/tex]
or, S = 7.85 m
Let us assume the arc subtends angle Ф at the center of the circle.
⇒ S = r Ф
or, Ф = [tex]\frac{S}{r} = \frac{7.85}{3} = 2.61[/tex]
⇒Ф = 2.61 radians
Now, 1 Radian = 57.2958 Degrees
⇒ 2. 62 Radian = 2.61 x ( 57.2958 Degrees) = 149.542 °
or, Ф = 149.542°
Hence, the measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°
