In circle M with m, angle, L, M, N, equals, 46, degreesm∠LMN=46 ∘ and L, M, equals, 14LM=14 units, find the length of arc, L, N LN⌢ . Round to the nearest hundredth.

To find the length of arc LN, we need to use the formula for the length of an arc, which is:

Arc length = (m∠ / 360) * 2πr

Where:

• m∠ is the measure of the angle in degrees, which is 46 degrees in this case.
• r is the radius of the circle, which is 14 units in this case.

So, substituting the given values into the formula, we get:

Arc length = (46 / 360) * 2π * 14

Now, we just need to calculate the above expression to find the length of arc LN.

Arc length = 0.12778 * 2 * 3.1416 * 14

Arc length = 11.30973 units

So, the length of arc LN is approximately 11.31 units when rounded to the nearest hundredth.

To find the length of arc LN, we need to use the formula for the length of an arc, which is:

Arc length = (m∠ / 360) * 2πr

Where:

• m∠ is the measure of the angle subtended by the arc at the center of the circle, in degrees
• r is the radius of the circle

Given that m∠LMN = 46 degrees and LM = 14 units (which is the radius of the circle), we can substitute these values into the formula:

Arc length = (46 / 360) * 2π * 14

Now, we just need to calculate the above expression to find the length of arc LN.

Arc length = 0.12778 * 2 * 3.14159 * 14 = 11.30973 units

Rounding to the nearest hundredth, the length of arc LN is approximately 11.31 units.