Question

In circle L with m^KLM 54 and KL= 10 units, find the length of arc KM.

Round to the nearest hundredth.

Answer 1

Given:

In circle L, measure of angle KLM is 54 degrees and KL = 10 units.

To find:

The length of arc KM.

Solution:

The formula for arc length is:

`s=2\pi r* (\theta)/(360^\circ)` ...(i)

Where, r is the radius of the circle and
`\theta` is the central angle in degrees.

The measure of KL is 10 units, it means the radius of the circle L is 10 units.

The measure of angle KLM is 54 degrees, it means the measure of central angle on arc KM is 54 degrees.

Putting
`\pi=3.14, r=10,\theta=54^\circ` in (i), we get

`s=2(3.14)(10)* (54^\circ)/(360^\circ)`

`s=20(3.14)* 0.15`

`s=9.42`

Therefore, the length of arc KM is 9.42 units.