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
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5degree and10 degree 10 cm apart on given map, what is the scale of the map?
answer
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Ah, the wonderful world of maps! Well, if two places on the ground that are 5 degrees apart are shown 10 cm apart on the map, then we can calculate the scale of the map.
So, let's do some math (brace yourself, it might be a little exciting).
If a 5-degree distance corresponds to a 10 cm distance on the map, then we can say that 10 cm is equal to 5 degrees.
Now, we need to figure out how many centimeters represent 1 degree, right?
We can set up a simple proportion:
10 cm / 5 degrees = X cm / 1 degree
Cross-multiplying and solving for X, we get:
X = (10 cm * 1 degree) / 5 degrees
Dragging out every last bit of math skill I've got, we find:
X = 2 cm
Ah, there you have it! The scale of the map is 1 degree equals 2 cm. So, if you draw something 2 cm apart on the map, you can imagine that it's actually 1 degree apart on the ground. Happy mapping!
To find the scale of the map, we need to calculate the distance between the two places in real life using the given information.
Given:
- On the map, the distance between the two places is 10 cm
- The latitude difference between the two places is 10° (5° north to 10° north)
First, we need to understand the relationship between the distance on the map and the distance in real life. The scale of a map represents the ratio of distances on the map to distances in real life.
In this case, we can assume that the scale is constant along the latitude lines. So, the distance between two latitude lines on the map will be equivalent to the distance between the two latitude lines in real life.
To calculate the distance between the two places in real life:
- We know that the latitude difference between the two places is 10°.
- The distance between two consecutive latitude lines on the Earth is approximately 111 km.
So, the distance between the two places in real life is:
10° * 111 km/° = 1110 km
Now, we can calculate the scale of the map by comparing the distance on the map to the distance in real life:
Scale = Distance on the map / Distance in real life
Scale = 10 cm / 1110 km
To express the scale in a more conventional form, we need to convert centimeters to kilometers:
1 cm = 1/100,000 km
Scale = (10 cm / 1110 km) * (1/100,000 km/1 cm)
Scale = 0.00009 km/cm
Therefore, the scale of the map is 1:0.00009, meaning that every 1 cm on the map represents a distance of 0.00009 km in real life.