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Answer :
To determine how many kilometers and miles 37° of latitude is on Earth, we use the concept of arc length. The arc length of a circle segment (in this case, a segment of Earth's latitude) can be calculated using the formula:
[tex]\[ \text{Arc length} = \text{radius} \times \text{radians} \][/tex]
We'll go through this step-by-step:
1. Convert Degrees to Radians:
Latitude is given in degrees. To find the arc length, we first need to convert these degrees to radians because the formula uses radians. The conversion factor is:
[tex]\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
For 37° of latitude, the conversion to radians is:
[tex]\[ 37 \times \left(\frac{\pi}{180}\right) \approx 0.6458 \text{ radians} \][/tex]
2. Calculate the Arc Length in Kilometers:
Given: Earth's radius is approximately 6400 kilometers.
Using the formula for arc length:
[tex]\[ \text{Arc length in km} = 6400 \times 0.6458 \approx 4132.94 \text{ kilometers} \][/tex]
3. Calculate the Arc Length in Miles:
Given: Earth's radius is approximately 4000 miles.
Again, use the formula:
[tex]\[ \text{Arc length in miles} = 4000 \times 0.6458 \approx 2583.09 \text{ miles} \][/tex]
Therefore, 37° of latitude on Earth is approximately 4132.94 kilometers or 2583.09 miles.
[tex]\[ \text{Arc length} = \text{radius} \times \text{radians} \][/tex]
We'll go through this step-by-step:
1. Convert Degrees to Radians:
Latitude is given in degrees. To find the arc length, we first need to convert these degrees to radians because the formula uses radians. The conversion factor is:
[tex]\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
For 37° of latitude, the conversion to radians is:
[tex]\[ 37 \times \left(\frac{\pi}{180}\right) \approx 0.6458 \text{ radians} \][/tex]
2. Calculate the Arc Length in Kilometers:
Given: Earth's radius is approximately 6400 kilometers.
Using the formula for arc length:
[tex]\[ \text{Arc length in km} = 6400 \times 0.6458 \approx 4132.94 \text{ kilometers} \][/tex]
3. Calculate the Arc Length in Miles:
Given: Earth's radius is approximately 4000 miles.
Again, use the formula:
[tex]\[ \text{Arc length in miles} = 4000 \times 0.6458 \approx 2583.09 \text{ miles} \][/tex]
Therefore, 37° of latitude on Earth is approximately 4132.94 kilometers or 2583.09 miles.
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