On the​ earth, 41degrees° of latitude is how many​ kilometers? how many​ miles? (Assume that the radius of the earth is 6400​ km, or 4000​ mi, approximately.)

On earth 41degrees° of latitude is approximately equal to enter your response in kilometers.

1 answer

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