Question

Determine the length of arc JL. A) 25/ 9 π B) 5 /13 π C) 25 /18 π D) 14 /17 π

Answer 1

Option C is the right choice where length of the arc is 25/18π.

Explanation:

Given:

Length of the radius of the circle,
`r` = 2 unit

Angle between the arc,
`\theta` = 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' =
`2\pi r* ((\theta)/(360))`

⇒
`a=2\pi r* ((\theta)/(360))`

⇒
`a=2\pi (2)* ((125)/(360))`

⇒
`a=4\pi * ((125)/(360))`

⇒
`a=(4\pi * 125)/(360)`

⇒
`a=(500\pi )/(360)`

⇒
`a=(50\pi )/(36)`

⇒
`a=(25\pi )/(18)` ... reducing to lowest term.

So,

The length of the arc JL is 25/18π and option C is the right choice.