Calculate the distance between latitude 4¤N and 14¤N of the equator on the same longitude 3¤E
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14 N-4 N=10.
To calculate the distance between two latitudes on the same longitude, you can use the Haversine formula, which takes into account the curvature of the Earth.
Step 1: Convert the latitudes from degrees to radians.
4°N = 4 * (π/180) radians
14°N = 14 * (π/180) radians
Step 2: Determine the radius of the Earth.
The average radius of the Earth is approximately 6,371 kilometers.
Step 3: Use the Haversine formula to calculate the distance.
haversine(d) = sin²((lat₂ - lat₁)/2) + cos(lat₁) * cos(lat₂) * sin²((long₂ - long₁)/2)
where:
- lat₁ and lat₂ are the latitudes in radians
- long₁ and long₂ are the longitudes in radians
Let's plug in the values and calculate the distance:
lat₁ = 4 * (π/180) radians
lat₂ = 14 * (π/180) radians
long₁ = 3 * (π/180) radians
long₂ = 3 * (π/180) radians
haversine(d) = sin²((14 * (π/180) - 4 * (π/180))/2) + cos(4 * (π/180)) * cos(14 * (π/180)) * sin²((3 * (π/180) - 3 * (π/180))/2)
After evaluating the equation, you will get the haversine of the distance.
Step 4: Calculate the actual distance.
The distance can be calculated using the following formula:
distance = 2 * radius * arcsin(sqrt(haversine(d)))
Using this formula, you can substitute the value of haversine(d) and the Earth's radius:
distance = 2 * 6,371 km * arcsin(sqrt(haversine(d)))
Calculate the value and you'll get the distance between the two latitudes on the same longitude, in kilometers.