WHAT IS THE DISTANCE BETWEEN LATITUDE 4'N AND 14'N ON THE SAME LONGITUDE 3.E?
Each degree of latitude is approximately 69 miles (111 kilometers) apart.
To find the distance between two latitudes on the same longitude, you can use the formula:
Distance = (Difference in Latitude) × (Length of 1° Latitude)
Since the two latitudes, 4'N and 14'N, are on the same longitude, we can calculate the distance between them:
Difference in Latitude = 14°N - 4°N = 10°
Next, we need to find the length of 1° latitude. The length of 1° latitude is approximately equal to 111 km (or about 69 miles) at the equator. However, the length of 1° latitude decreases as you move away from the equator.
To be more accurate, we can use the following approximation:
Length of 1° Latitude = 111 km × cos(latitude)
Using the latitude of 14°N to approximate the distance:
Length of 1° Latitude = 111 km × cos(14°N)
Calculating the cosine value:
cos(14°N) ≈ 0.970
Length of 1° Latitude ≈ 111 km × 0.970 ≈ 107.97 km (approximately)
Now, we can calculate the distance between the two latitudes:
Distance ≈ (Difference in Latitude) × (Length of 1° Latitude)
≈ 10° × 107.97 km
≈ 1,079.7 km (approximately)
Therefore, the distance between latitude 4'N and 14'N on the same longitude (3°E) is approximately 1,079.7 km.
To calculate the distance between two points on the Earth's surface given their latitude and longitude, you can use the Haversine formula. The formula is based on great-circle distance, which is the shortest distance between two points on a sphere.
Here are the steps to calculate the distance:
1. Convert the latitude and longitude from degrees to radians.
- Latitude 4'N = 4°N = 4 * (π/180) radians ≈ 0.0698132 radians
- Latitude 14'N = 14°N = 14 * (π/180) radians ≈ 0.2443461 radians
- Longitude 3.E doesn't provide enough information. The letter "E" denotes East, so we assume 3°E.
2. Use the Haversine formula:
- Distance = 2 * r * arcsin(sqrt(sin^2((lat2 - lat1)/2) + cos(lat1) * cos(lat2) * sin^2((lon2 - lon1)/2)))
In this formula:
- r is the radius of the Earth (mean Earth radius is approximately 6,371 kilometers or 3,959 miles).
- lat1 and lat2 are the latitudes in radians.
- lon1 and lon2 are the longitudes in radians.
Applying the values:
- Latitude difference = (14 * (π/180)) - (4 * (π/180)) = 0.1745329 radians
- Longitude difference = 3°E = 3 * (π/180) radians ≈ 0.0523599 radians
3. Plug the values into the formula and calculate the distance:
- Distance = 2 * 6371 * arcsin(sqrt(sin^2(0.1745329/2) + cos(0.0698132) * cos(0.2443461) * sin^2(0.0523599/2)))
Evaluating this equation will give you the distance between the two latitudes on the same longitude.
Please note that this calculation gives the distance along the surface of the Earth, assuming a perfectly spherical shape. The actual distance may vary depending on the Earth's shape and local topography.
14°N - 4°N = 10°
10×111km = 1110km