Given:
In a circle M with the measure of ∠LMN = 102° and LM = 11 units.
We need to determine the arc length of LN
Arc length of LN:
The arc length of LN can be determined using the formula,
[tex]{arc \ length}=2 \pi r\left(\frac{\theta}{360}\right)[/tex]
where r is the radius and [tex]\theta[/tex] is the central angle.
Substituting [tex]r=11[/tex] and [tex]\theta=102[/tex] in the above formula, we get;
[tex]{arc \ length}=2 (3.14)(11)\left(\frac{102}{360}\right)[/tex]
Simplifying, we get;
[tex]{arc \ length}=69.08\left(\frac{102}{360}\right)[/tex]
[tex]{arc \ length}=19.573[/tex]
Rounding off to the nearest hundredth, we get;
[tex]{arc \ length}=19.57[/tex]
Thus, the arc length of LN is 19.57 units.
