Respuesta :
To find the shortest distance between two points on the Earth's surface with given longitudes, you can use the following formula:
\[ \text{Shortest distance} = R \times \Delta\theta \]
where:
- \( R \) is the radius of the Earth (approximately 6,371 kilometers),
- \( \Delta\theta \) is the absolute difference in longitudes.
In this case, the longitudes are given in degrees, but they need to be converted into a common reference direction. Since longitudes are measured eastward from the prime meridian, convert the longitude of Q from west to east:
\[ \text{Longitude of Q (east)} = 360° - \text{Longitude of Q (west)} \]
Now, calculate the absolute difference in longitudes (\( \Delta\theta \)) and use the formula to find the shortest distance.
First, convert the longitude of Q from west to east:
\[ \text{Longitude of Q (east)} = 360° - \text{Longitude of Q (west)} \]
\[ \text{Longitude of Q (east)} = 360° - 171° = 189°E \]
Now, calculate the absolute difference in longitudes:
\[ \Delta\theta = \text{Longitude of Q (east)} - \text{Longitude of P} \]
\[ \Delta\theta = 189° - 152° = 37° \]
Using the formula for the shortest distance:
\[ \text{Shortest distance} = R \times \Delta\theta \]
\[ \text{Shortest distance} = 6371 \, \text{km} \times 37° \]
Calculate this to find the shortest distance between P and Q on the Earth's surface.
\[ \text{Shortest distance} = R \times \Delta\theta \]
where:
- \( R \) is the radius of the Earth (approximately 6,371 kilometers),
- \( \Delta\theta \) is the absolute difference in longitudes.
In this case, the longitudes are given in degrees, but they need to be converted into a common reference direction. Since longitudes are measured eastward from the prime meridian, convert the longitude of Q from west to east:
\[ \text{Longitude of Q (east)} = 360° - \text{Longitude of Q (west)} \]
Now, calculate the absolute difference in longitudes (\( \Delta\theta \)) and use the formula to find the shortest distance.
First, convert the longitude of Q from west to east:
\[ \text{Longitude of Q (east)} = 360° - \text{Longitude of Q (west)} \]
\[ \text{Longitude of Q (east)} = 360° - 171° = 189°E \]
Now, calculate the absolute difference in longitudes:
\[ \Delta\theta = \text{Longitude of Q (east)} - \text{Longitude of P} \]
\[ \Delta\theta = 189° - 152° = 37° \]
Using the formula for the shortest distance:
\[ \text{Shortest distance} = R \times \Delta\theta \]
\[ \text{Shortest distance} = 6371 \, \text{km} \times 37° \]
Calculate this to find the shortest distance between P and Q on the Earth's surface.
