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Answer :
To find the distance between two cities, A and B, using the given angle and the radius of the Earth, you can follow these steps:
1. Understand the given values:
- The angle between the two cities, denoted as [tex]\(\theta\)[/tex], is given as [tex]\(35^\circ\)[/tex].
- The radius of the Earth is approximately 4000 miles.
2. Convert the angle from degrees to radians:
- Since calculations involving circular motion or arcs typically use radians, you'll need to convert the angle from degrees to radians.
- Use the conversion formula: [tex]\(\text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right)\)[/tex].
- Thus, [tex]\(\theta\)[/tex] in radians is [tex]\(35 \times \left(\frac{\pi}{180}\right)\)[/tex].
3. Calculate the arc distance:
- The arc distance, which represents the distance between the two cities along the Earth's surface, can be found using the formula: [tex]\(\text{distance} = \text{radius} \times \text{angle in radians}\)[/tex].
- Substitute the known values: [tex]\(\text{distance} = 4000 \times \left(35 \times \left(\frac{\pi}{180}\right)\right)\)[/tex].
4. Round to the nearest mile:
- After performing the multiplication, round the calculated distance to the nearest whole mile.
By following these steps, the distance between cities A and B is approximately 2443 miles.
1. Understand the given values:
- The angle between the two cities, denoted as [tex]\(\theta\)[/tex], is given as [tex]\(35^\circ\)[/tex].
- The radius of the Earth is approximately 4000 miles.
2. Convert the angle from degrees to radians:
- Since calculations involving circular motion or arcs typically use radians, you'll need to convert the angle from degrees to radians.
- Use the conversion formula: [tex]\(\text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right)\)[/tex].
- Thus, [tex]\(\theta\)[/tex] in radians is [tex]\(35 \times \left(\frac{\pi}{180}\right)\)[/tex].
3. Calculate the arc distance:
- The arc distance, which represents the distance between the two cities along the Earth's surface, can be found using the formula: [tex]\(\text{distance} = \text{radius} \times \text{angle in radians}\)[/tex].
- Substitute the known values: [tex]\(\text{distance} = 4000 \times \left(35 \times \left(\frac{\pi}{180}\right)\right)\)[/tex].
4. Round to the nearest mile:
- After performing the multiplication, round the calculated distance to the nearest whole mile.
By following these steps, the distance between cities A and B is approximately 2443 miles.
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