The city of Washington in United States of America and the city of Lima in Peru lie on the same longitude but are on latitudes \( 38.88^{\circ} \mathrm{N} \) and \( 12.04^{\circ} \mathrm{S} \) respectively. Given that the earth is a sphere with a radius of 6371 km , estimate the distance, in km , between the two cities.

To estimate the distance between Washington and Lima, first calculate the difference in latitude: \[ \text{Difference in latitude} = 38.88^\circ N + 12.04^\circ S = 38.88 + 12.04 = 50.92^\circ \] Now, convert this latitude difference into radians since distance calculations typically use radians. The conversion factor is \(\pi \, \text{radians} = 180^\circ\): \[ \text{Difference in radians} = \frac{50.92 \times \pi}{180} \approx 0.887 \, \text{radians} \] Next, we can find the arc length (distance) on the surface of the Earth using the formula: \[ \text{Distance} = R \times \theta \] where \(R\) is the radius of the Earth (approximately \(6371 \, \text{km}\)) and \(\theta\) is the difference in radians: \[ \text{Distance} = 6371 \times 0.887 \approx 5642 \, \text{km} \] So, the estimated distance between Washington and Lima is approximately **5642 kilometers**.