Find the length of the arc for a circle with a radius of 7 mi and a central angle of 210 degrees round your answer to the tenths place

Answer 1

To find the length of an arc in a circle, you can use the formula:

$$L=r\theta$$

where:

• $L$ is the arc length,
• $r$ is the radius of the circle,
• $\theta$ is the central angle in radians.

First, you need to convert the angle from degrees to radians. The conversion formula is:

$$\theta \text{ (in radians)}=\theta \text{ (in degrees)}\times \frac{\pi }{180}$$

For a central angle of 210 degrees:

$$\theta =210\times \frac{\pi }{180}=\frac{210\pi }{180}=\frac{7\pi }{6}$$

Now, substitute the values into the arc length formula. The radius $r=7$ miles, and now we have $\theta =\frac{7\pi }{6}$:

$$L=7\times \frac{7\pi }{6}=\frac{49\pi }{6}$$

Now, calculate $\frac{49\pi }{6}$:

Using $\pi \approx 3.14159$:

$$L\approx \frac{49\times 3.14159}{6}\approx \frac{153.93851}{6}\approx 25.65642$$

Rounding this to the tenths place gives:

$$L\approx 25.7\text{ miles}$$

Thus, the length of the arc is approximately 25.7 miles.

Answer 2

452.4 mi
43.2 mi
44 mi
75.4 mi

Answer 3

It seems you're providing a list of distances, possibly as options or for some comparison. However, without any additional context or instructions, it's unclear what you would like me to do with these values.

If you have a specific question or task in mind regarding these distances (e.g., calculating a total, finding the average, etc.), please let me know!