Question

The circle below has center k , and its radius is 3 cm Given that m∠LKM =70° , find the length of the major arcLNM

Answer 1

The length of the major arc LNM is $\frac{29}{6}\pi \ cm$

Length of an arc

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

$Length \ of \ major\ arc \ LNM = \frac{Reflex$

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

$Length \ of \ major\ arc \ LNM = \frac{290 ^\circ }{360 ^\circ} \times 2\pi \times 3$

Then,

$Length \ of \ major\ arc \ LNM = \frac{1740\pi}{360}$

$Length \ of \ major\ arc \ LNM = \frac{29}{6} \pi \ cm$

Hence, the length of the major arc LNM is $\frac{29}{6}\pi \ cm$

Learn more on calculating length of an arc here: brainly.com/question/2005046