Answer:
Option C is the right choice where length of the arc is 25/18π.
Step-by-step explanation:
Given:
Length of the radius of the circle, [tex]r[/tex] = 2 unit
Angle between the arc, [tex]\theta[/tex] = 125°
We have to find the arc length.
Let the arc length JL be "a" unit.
Formula to be used:
Arc length = (Circumference times angle ) / 360°
Using the above formula and plugging the values.
⇒ Arc length, JL, 'a' = [tex]2\pi r\times (\frac{\theta}{360})[/tex]
⇒ [tex]a=2\pi r\times (\frac{\theta}{360})[/tex]
⇒ [tex]a=2\pi (2)\times (\frac{125}{360})[/tex]
⇒ [tex]a=4\pi \times (\frac{125}{360})[/tex]
⇒ [tex]a=\frac{4\pi \times 125}{360}[/tex]
⇒ [tex]a=\frac{500\pi }{360}[/tex]
⇒ [tex]a=\frac{50\pi }{36}[/tex]
⇒ [tex]a=\frac{25\pi }{18}[/tex] ... reducing to lowest term.
So,
The length of the arc JL is 25/18π and option C is the right choice.
