Question

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

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:

$s=2\pi r\times \dfrac{\theta}{360^\circ}$          ...(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

$s=2(3.14)(10)\times \dfrac{54^\circ}{360^\circ}$

$s=20(3.14)\times 0.15$

$s=9.42$

Therefore, the length of arc KM is 9.42 units.