The length of the major arc LNM is [tex]\frac{29}{6}\pi \ cm[/tex]
From the question,
We are to determine the value of the length of the major arc LNM
The length of the major arc LNM can be calculated using the formula
[tex]Length \ of \ major\ arc \ LNM = \frac{Reflex \ <LKM}{360 ^\circ} \times 2\pi r[/tex]
Where r is the radius
First, we will determine the value of the reflex ∠LKM
Reflex ∠LKM + ∠LKM = 360° (Sum of angles at a point)
From the given information,
∠LKM = 70°
Then,
Reflex ∠LKM + 70° = 360°
Reflex ∠LKM = 360° - 70°
Reflex ∠LKM = 290°
Also, from the question
r = 3 cm
Now, putting the parameters into the formula, we get
[tex]Length \ of \ major\ arc \ LNM = \frac{290 ^\circ }{360 ^\circ} \times 2\pi \times 3[/tex]
Then,
[tex]Length \ of \ major\ arc \ LNM = \frac{1740\pi}{360}[/tex]
[tex]Length \ of \ major\ arc \ LNM = \frac{29}{6} \pi \ cm[/tex]
Hence, the length of the major arc LNM is [tex]\frac{29}{6}\pi \ cm[/tex]
Learn more on calculating length of an arc here: https://brainly.com/question/2005046
