Question

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the circle below has center k, and its radius is 5 cm. given that m∠lkm = 70°, find the length of the minor arc lm. give an exact answer in terms of π, and be sure to include the correct unit in your answer. length of minor arc lm:

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc of a circle is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. First, we need to convert the angle from degrees to radians. The conversion formula is $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$.

Step2: Convert the angle to radians

Given $\theta_{deg}=70^{\circ}$, then $\theta_{rad}=\frac{\pi}{180}\times70=\frac{7\pi}{18}$ radians. The radius $r = 5$ cm.

Step3: Calculate the arc - length

Substitute $r = 5$ cm and $\theta=\frac{7\pi}{18}$ into the arc - length formula $s=r\theta$. So $s = 5\times\frac{7\pi}{18}=\frac{35\pi}{18}$ cm.

Answer:

$\frac{35\pi}{18}$ cm