Thank you for visiting 26 A circle has a radius of 8 cm Suppose an arc on the circle has a length of 27 cm What is the measure. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
- Calculate the central angle in radians using the formula $\theta = \frac{s}{r}$, where $s = 27$ cm and $r = 8$ cm, resulting in $\theta = 3.375$ radians.
- Convert $45$ degrees to radians by multiplying by $\frac{\pi}{180}$, which simplifies to $\frac{\pi}{4}$ radians.
- Convert $\frac{7\pi}{6}$ radians to degrees by multiplying by $\frac{180}{\pi}$, which equals $210$ degrees.
- State the final answers: The central angle is $3.375$ radians, $45$ degrees is $\frac{\pi}{4}$ radians, and $\frac{7\pi}{6}$ radians is $210$ degrees. $\boxed{3.375 \text{ radians}, \frac{\pi}{4} \text{ radians}, 210 \text{ degrees}}$
### Explanation
1. Find the central angle in radians.
We are given a circle with radius $r = 8$ cm and an arc length $s = 27$ cm. We need to find the central angle $\theta$ in radians. The formula relating arc length, radius, and central angle is $s = r\theta$.
2. Calculate the central angle.
To find the central angle $\theta$, we can rearrange the formula as $\theta = \frac{s}{r}$. Substituting the given values, we have $\theta = \frac{27}{8} = 3.375$ radians.
3. Convert 45 degrees to radians.
Next, we need to convert $45$ degrees to radians. To do this, we multiply by $\frac{\pi}{180}$. So, $45 \cdot \frac{\pi}{180} = \frac{45\pi}{180} = \frac{\pi}{4}$ radians.
4. Convert 7pi/6 radians to degrees.
Finally, we need to convert $\frac{7\pi}{6}$ radians to degrees. To do this, we multiply by $\frac{180}{\pi}$. So, $\frac{7\pi}{6} \cdot \frac{180}{\pi} = \frac{7 \cdot 180}{6} = 7 \cdot 30 = 210$ degrees.
5. State the final answers.
Therefore, the central angle is $3.375$ radians, $45$ degrees is equal to $\frac{\pi}{4}$ radians, and $\frac{7\pi}{6}$ radians is equal to $210$ degrees.
### Examples
Understanding radians and degrees is crucial in fields like astronomy, where angles are used to measure the positions of stars and planets. For example, astronomers use radians to describe the angular size of celestial objects or the angular distance between them.
- Convert $45$ degrees to radians by multiplying by $\frac{\pi}{180}$, which simplifies to $\frac{\pi}{4}$ radians.
- Convert $\frac{7\pi}{6}$ radians to degrees by multiplying by $\frac{180}{\pi}$, which equals $210$ degrees.
- State the final answers: The central angle is $3.375$ radians, $45$ degrees is $\frac{\pi}{4}$ radians, and $\frac{7\pi}{6}$ radians is $210$ degrees. $\boxed{3.375 \text{ radians}, \frac{\pi}{4} \text{ radians}, 210 \text{ degrees}}$
### Explanation
1. Find the central angle in radians.
We are given a circle with radius $r = 8$ cm and an arc length $s = 27$ cm. We need to find the central angle $\theta$ in radians. The formula relating arc length, radius, and central angle is $s = r\theta$.
2. Calculate the central angle.
To find the central angle $\theta$, we can rearrange the formula as $\theta = \frac{s}{r}$. Substituting the given values, we have $\theta = \frac{27}{8} = 3.375$ radians.
3. Convert 45 degrees to radians.
Next, we need to convert $45$ degrees to radians. To do this, we multiply by $\frac{\pi}{180}$. So, $45 \cdot \frac{\pi}{180} = \frac{45\pi}{180} = \frac{\pi}{4}$ radians.
4. Convert 7pi/6 radians to degrees.
Finally, we need to convert $\frac{7\pi}{6}$ radians to degrees. To do this, we multiply by $\frac{180}{\pi}$. So, $\frac{7\pi}{6} \cdot \frac{180}{\pi} = \frac{7 \cdot 180}{6} = 7 \cdot 30 = 210$ degrees.
5. State the final answers.
Therefore, the central angle is $3.375$ radians, $45$ degrees is equal to $\frac{\pi}{4}$ radians, and $\frac{7\pi}{6}$ radians is equal to $210$ degrees.
### Examples
Understanding radians and degrees is crucial in fields like astronomy, where angles are used to measure the positions of stars and planets. For example, astronomers use radians to describe the angular size of celestial objects or the angular distance between them.
Thank you for reading the article 26 A circle has a radius of 8 cm Suppose an arc on the circle has a length of 27 cm What is the measure. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
