An arc of a circle measures 52°. If the radius of a circle is 5 cm, how long is ...

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marcobrain @marcobrain

October 2022 1 21 Report

An arc of a circle measures 52°. If the radius of a circle is 5 cm, how long is the arc?

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sherlockinthemaking

Answer:

The arc has a length of about 4.5356°.

Step-by-step explanation:

To find the length of an arc, use the formula $s = 2\pi r ( \frac{\theta}{360})$ in which $s$ is the length of the arc, $r$ is the radius of the circle, and $\theta$ is the degrees or radians of the central angle. The formula is for the $\theta$ in degrees. However, if it is in radians, use the formula $s = \theta r$ .

Right now our central angle is in degrees so we use the first formula stated above.

We do the following:

$s = 2\green{\pi}\blue{r}( \frac{\red{\theta}}{360} ) \\ s = 2 \times \green{3.14}\times\blue{5}\times\frac{\red{52}}{360} \\ s = \frac{2 \times 3.14 \times 5 \times 52}{360} \\ s = \frac{1632.8}{360} \\ s = 4.5356$

We conclude that the arc length is 4.5356 degrees long.

Hope this helps and #CarryOnLearning!

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