To calculate the distance corresponding to 41 degrees of latitude, we can use the formula that relates the angle in degrees to the distance on the surface of a sphere. Given that the radius of Earth is approximately 6400 km, the distance \( D \) can be calculated using the formula:
\[ D = r \times \theta \]
where:
- \( r \) is the radius of the Earth,
- \( \theta \) is the angle in radians.
First, we need to convert degrees into radians. The conversion factor from degrees to radians is:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
For 41 degrees, the conversion to radians is:
\[ \theta = 41 \times \frac{\pi}{180} \approx 0.7156 \text{ radians} \]
Now, we can calculate the distance:
\[ D = 6400 , \text{km} \times 0.7156 \approx 4575.36 , \text{km} \]
So, 41 degrees of latitude is approximately 4575.36 kilometers.
Next, to convert this distance to miles, we can use the conversion factor that 1 kilometer is approximately equal to 0.621371 miles:
\[ D_{\text{miles}} = 4575.36 , \text{km} \times 0.621371 , \text{miles/km} \approx 2845.88 , \text{miles} \]
Therefore, 41 degrees of latitude is approximately:
- 4575.36 kilometers
- 2845.88 miles