Question

Calculate the distance between Lagos (40°n) and Cairo (30°n)

Answer 1

To calculate the distance between Lagos and Cairo, we can use the latitude and longitude coordinates of the two cities.

The latitude of Lagos is 40°N and the latitude of Cairo is 30°N.

The distance between the two cities can be calculated using the Haversine formula, which is a formula used to calculate the great-circle distance between two points on a sphere (in this case, the Earth's surface).

Using the Haversine formula, the distance (D) between two points with latitudes (lat1 and lat2) can be calculated as:

D = 2 * R * arcsin(sqrt(sin^2((lat2 - lat1) / 2) + cos(lat1) * cos(lat2) * sin^2((lon2 - lon1) / 2)))

Where R is the radius of the Earth (approximately 6,371 kilometers).

Substituting the values for Lagos (40°N) and Cairo (30°N) into the formula, we get:

D = 2 * 6,371 * arcsin(sqrt(sin^2((30° - 40°) / 2) + cos(40°) * cos(30°) * sin^2((0° - 0°) / 2)))

Calculating this, we get:

D = 2 * 6,371 * arcsin(sqrt(sin^2((-10°) / 2) + cos(40°) * cos(30°) * sin^2(0° / 2)))

D = 2 * 6,371 * arcsin(sqrt(sin^2(-5°) + cos(40°) * cos(30°) * sin^2(0°)))

Using trigonometric identities, we can simplify the expression further:

D = 2 * 6,371 * arcsin(sqrt(sin^2(-5° / 2) + cos(40°) * cos(30°) * sin^2(0°)))

D = 2 * 6,371 * arcsin(sqrt(sin^2(-2.5°) + cos(40°) * cos(30°) * sin^2(0°)))

D = 2 * 6,371 * arcsin(sqrt(sin^2(-2.5°) + cos(40°) * cos(30°) * 0))

Since sin(0°) = 0, the term sin^2(0°) becomes 0.

D = 2 * 6,371 * arcsin(sqrt(sin^2(-2.5°) + 0))

D = 2 * 6,371 * arcsin(sqrt(sin^2(-2.5°)))

D = 2 * 6,371 * arcsin(sqrt((-sin(2.5°))^2))

Using a scientific calculator or an online calculator, we can find that:

D ≈ 2 * 6,371 * arcsin(sqrt(0.00213134))

D ≈ 2 * 6,371 * arcsin(0.046181)

D ≈ 2 * 6,371 * 0.046420

D ≈ 2 * 6,371 * 0.046420

D ≈ 2 * 6,371 * 0.046420

D ≈ 2 * 6,371 * 0.046420

D ≈ 6,371 * 0.092840

D ≈ 592.17 kilometers

Therefore, the approximate distance between Lagos and Cairo is 592.17 kilometers.