To calculate the distance corresponding to 77 degrees of latitude, we can use the following information:
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The Earth's radius is approximately 6400 km.
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The circumference of the Earth can be calculated using the formula: \[ \text{Circumference} = 2 \pi r \] where \( r \) is the radius of the Earth.
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Since latitude lines are parallel and each degree of latitude corresponds to the same distance on the ground, we can find the distance for 77 degrees by calculating the fraction of the Earth's circumference that corresponds to 77 degrees.
Step 1: Calculate the circumference of the Earth
Using the radius of 6400 km: \[ \text{Circumference} = 2 \pi (6400 , \text{km}) \approx 2 \times 3.14159 \times 6400 \approx 40212 , \text{km} \]
Step 2: Calculate the distance for 77 degrees
The fraction of the full circumference for 77 degrees is: \[ \text{Distance at 77 degrees} = \left(\frac{77}{360}\right) \times \text{Circumference} \] \[ \text{Distance at 77 degrees} = \left(\frac{77}{360}\right) \times 40212 , \text{km} \approx \frac{77 \times 40212}{360} \approx 8655.2 , \text{km} \]
Step 3: Convert kilometers to miles
To convert kilometers to miles, we use the conversion factor \( 1 , \text{km} \approx 0.621371 , \text{miles} \): \[ 8655.2 , \text{km} \times 0.621371 , \text{miles/km} \approx 5372.7 , \text{miles} \]
Final Results
The distance on Earth at 77 degrees of latitude is approximately:
- 8655.2 km
- 5372.7 miles
So, your responses should be:
- On earth, 77 degrees of latitude is approximately equal to 8655.2 kilometers.
- This is approximately equal to 5372.7 miles.