Calculate distance between Lagos (4N) and Cairo (30N)
each degree of latitude is about 111 km, so ...
To calculate the distance between two points on the Earth's surface, such as Lagos (4°N) and Cairo (30°N), you need to use the latitude and longitude coordinates of these two locations. Here's how you can calculate the distance:
Step 1: Determine the latitude and longitude coordinates of Lagos and Cairo.
Lagos: Latitude = 4°N, Longitude = unknown (we need this information)
Cairo: Latitude = 30°N, Longitude = unknown (we need this information)
Step 2: Find the longitude difference between Lagos and Cairo.
In this case, we need to know the longitude coordinates of Lagos and Cairo to find the difference. If you have the specific longitude coordinates, subtract Lagos' longitude from Cairo's longitude. The resulting value will be the longitude difference.
Step 3: Use the Haversine formula to calculate the distance.
The Haversine formula is commonly used to calculate the distances between two points on the surface of a sphere (like Earth). It takes into account the Earth's radius and the latitude and longitude coordinates of the two points.
The Haversine formula is as follows:
distance = 2 * radius * arcsin(√(sin²((lat2 - lat1) / 2) + cos(lat1) * cos(lat2) * sin²((lon2 - lon1) / 2)))
In this formula:
- distance is the great circle distance between two points
- radius is the Earth's radius (approximately 6,371 kilometers or 3,959 miles)
- lat1 and lon1 are the latitude and longitude coordinates of the first point
- lat2 and lon2 are the latitude and longitude coordinates of the second point
Plug in the latitude and longitude values you have for Lagos and Cairo into this formula to calculate the distance.
To calculate the distance between Lagos (4N) and Cairo (30N), you can use the haversine formula, which is the most commonly used method for calculating the distance between two points on the surface of a sphere (such as the Earth) given their longitudes and latitudes.
Here are the steps to calculate the distance:
Step 1: Convert the latitudes and longitudes from degrees to radians.
Lagos: Latitude = 4 degrees, Longitude = 0 degrees
Cairo: Latitude = 30 degrees, Longitude = 0 degrees
To convert degrees to radians, you can use the formula:
radians = degrees * (π/180)
Lagos: Latitude = 4 * π/180 radians, Longitude = 0 * π/180 radians
Cairo: Latitude = 30 * π/180 radians, Longitude = 0 * π/180 radians
Step 2: Calculate the difference in latitudes and longitudes.
Difference in latitude = Cairo latitude - Lagos latitude
Difference in longitude = Cairo longitude - Lagos longitude
Step 3: Apply the haversine formula to calculate the distance.
a = sin²(Δlat/2) + cos(Lagos lat) * cos(Cairo lat) * sin²(Δlon/2)
c = 2 * atan2(sqrt(a), sqrt(1-a))
distance = R * c, where R is the radius of the Earth (approximately 6371 kilometers or 3959 miles)
Let's substitute the values into the formula and calculate the distance:
Lagos Latitude = 4 * π/180 = 0.06981317008 radians
Cairo Latitude = 30 * π/180 = 0.5235987756 radians
Difference in latitude = 0.5235987756 - 0.06981317008 = 0.4537856056 radians
Difference in longitude = 0 degrees
Using the haversine formula:
a = sin²(0.4537856056/2) + cos(0.06981317008) * cos(0.5235987756) * sin²(0/2)
c = 2 * atan2(sqrt(a), sqrt(1-a))
distance = 3959 * c (assuming miles as the unit)
Calculating the values:
a = 0.1406342495
c = 0.2969381863
distance = 3959 * 0.2969381863 ≈ 1174.8 miles
Therefore, the approximate distance between Lagos and Cairo is approximately 1174.8 miles.