If two places on the ground that are located 5 degree North and 10 degree North are shown 10 cm apart on a given map what is the scale of the map
If two places on the ground that are located 5 degree North and 10 degree North are shown 10 cm apart on a given map what is the scale of the map
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Geography answer
If two places on the ground that are located 5 degree north and 10 degree north are shown 10 cm apart on given map,what is the scale of the map
To determine the scale of a map, you need to know the distance on the map and the corresponding distance in the real world. In this case, we have the distance on the map (10 cm) and the difference in latitude between the two places (5 degrees). We can use these values to calculate the scale of the map.
The distance between the two places on the map (10 cm) represents the difference in latitude (5 degrees) in the real world. Therefore, we need to find the ratio between the distance on the map and the corresponding distance in the real world.
To calculate the scale, you can use the following formula:
Scale = Distance on the Map / Distance in the Real World
In this case, the Distance on the Map is 10 cm and the Distance in the Real World is 5 degrees. The units need to be consistent for the calculation, so we need to convert the 5 degrees to a linear measurement.
To convert the degrees to a linear measurement, we need to know the circumference of the Earth (since latitude represents a circle around the Earth). The Earth's circumference is approximately 40,075 kilometers.
To convert from degrees to kilometers, we can use the following formula:
1 degree = (Circumference of Earth) / 360 degrees
Therefore, 5 degrees would be:
5 degrees = (40,075 km) / 360 degrees
Once we have the linear measurement (in kilometers), we can proceed with the calculation:
Scale = Distance on the Map / Distance in the Real World
Scale = 10 cm / (5 degrees * (40,075 km / 360 degrees))
By simplifying the expression:
Scale = 10 cm / (5 degrees * 111.319 km/degree)
Now, we can calculate the scale:
Scale = 10 cm / (5 * 111.319 km/degree)
Scale = 10 cm / (556.595 km/degree)
Scale ≈ 0.018
Therefore, the scale of the map is approximately 1:55, which means that 1 cm on the map represents an actual distance of 55 km.