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:
[tex]s=2\pi r\times \dfrac{\theta}{360^\circ}[/tex] ...(i)
Where, r is the radius of the circle and [tex]\theta [/tex] 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 [tex]\pi=3.14, r=10,\theta=54^\circ[/tex] in (i), we get
[tex]s=2(3.14)(10)\times \dfrac{54^\circ}{360^\circ}[/tex]
[tex]s=20(3.14)\times 0.15[/tex]
[tex]s=9.42[/tex]
Therefore, the length of arc KM is 9.42 units.
