Calculate the approximate distance in kilometre b\w town x (24 degree n) and town y (15 degree s located on the same longitude
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Calculate the approximate distance in km between town A (24n) and town B (15s) located on the same longitude
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To calculate the approximate distance between two towns located on the same longitude, you can use the formula for calculating the distance between two points on a sphere (in this case, Earth). The formula is called the haversine formula.
Here are the steps to calculate the distance between Town X and Town Y:
1. Convert the latitude from degrees to radians. To convert degrees to radians, multiply the degree value by π/180.
- Latitude of Town X: 24 degrees N, so it remains positive: 24 × π/180 radians
- Latitude of Town Y: 15 degrees S, so convert it to negative: -15 × π/180 radians
2. Calculate the difference in latitude between the two towns. Subtract the latitude of Town Y from the latitude of Town X.
3. Assume the Earth's radius is approximately 6,371 kilometers. This value represents the average radius of the Earth.
4. Use the haversine formula to calculate the distance between the two towns:
- Distance = 2 × radius × arcsin(sqrt(sin²(Δlat/2) + cos(lat₁) × cos(lat₂) × sin²(Δlong/2)))
- Δlat = Difference in latitude
- radius = Earth's radius (6,371 km)
- lat₁ = Latitude of Town X in radians
- lat₂ = Latitude of Town Y in radians
- Δlong = Difference in longitude (since both towns are on the same longitude, Δlong will be zero)
5. Simplify the equation using the given values and calculate the distance.
Let's plug in the values and calculate the approximate distance between Town X and Town Y:
Latitude of Town X: 24 × π/180 radians = 0.4189 radians
Latitude of Town Y: -15 × π/180 radians = -0.2618 radians
Difference in latitude (Δlat): 0.4189 - (-0.2618) = 0.6807 radians
Difference in longitude (Δlong): 0 (since they are on the same longitude)
Using the haversine formula:
Distance = 2 × 6,371 km × arcsin(sqrt(sin²(0.6807/2) + cos(0.4189) × cos(-0.2618) × sin²(0/2)))
Now, calculate the expression inside the arcsin:
sqrt(sin²(0.6807/2) + cos(0.4189) × cos(-0.2618) × sin²(0/2)) ≈ 0.0793
Thus, the distance between Town X and Town Y is approximately:
Distance = 2 × 6,371 km × arcsin(0.0793) ≈ 2 × 6,371 km × 0.0793 ≈ 1,007 km
Therefore, the approximate distance between Town X and Town Y is around 1,007 kilometers.