To calculate the distance between Lagos (4°N) and Cairo (30°N) along the surface of the Earth, you can use the formula for the arc length on the surface of a sphere.
-
Convert the latitude difference to radians:
- The difference in latitude = \(30°N - 4°N = 26°\).
- Convert degrees to radians using the formula: \[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \] \[ 26° \approx 26 \times \left(\frac{\pi}{180}\right) \approx 0.4538 \text{ radians} \]
-
Calculate the distance:
- The Earth's average radius is approximately 6,371 kilometers.
- The arc length \(d\) can be calculated using the formula:
\[
d = r \theta
\]
where:
- \(r\) is the radius of the Earth (6,371 km),
- \(\theta\) is the angle in radians.
So, substituting the values: \[ d \approx 6371 \times 0.4538 \approx 2886.67 \text{ kilometers} \]
Therefore, the distance between Lagos and Cairo along the Earth's surface is approximately 2,887 kilometers.