Introduction to Mapping Science
Exercise #4 – Size, Shape and Location on Earth
Name:_______________________
1. On the graph use Cartesian coordinates to locate the following points. Assume that each grid square
represents one unit.
Point
1
2
3
4
X
5.5
-3.5
-7.5
5.0
Y
6.6
-4.5
2.0
-3.5
2. What is the distance between points 1 and 2?_________ 3 and 4?__________4 and 2?__________
SHOW YOUR WORK:
Intro to Mapping and GIS F05 Exercise 4
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3. For each location on the map [1-5] write its latitude and longitude in the following table.
Point
Latitude
Longitude
1
2
3
4
5
Intro to Mapping and GIS F05 Exercise 4
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4.
Convert each of the following locations to decimal degrees: .
1.
2.
3.
40̊ 30’ 15” N
45̊ 25’ 05” S
10̊ 35’ 15” N
Point
75̊ 45’ 21” W
35̊ 55’ 01” E
55̊ 25’ 18” E
Latitude
Longitude
1
2
3
Show your work:
Intro to Mapping and GIS F05 Exercise 4
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5 - Great Distance Measurements
When measuring long distances we need to account for the curvature of the earth. In this case the procedure is to
calculate the number of degrees of great circle arc between the two places and then convert the arc measure, which is in
degrees, to distance measure by multiplying by 69 [for converting to miles].
Given the latitude and longitude of two places, use the following formula to determine the number of degrees in the arc of
the great circle connecting the two places:

 Arccos ((Sine(Lat1)*Sine(Lat2)) + (Cosine(Lat1)*Cosine(Lat2) * Cosine(|Long1 - Long2|)))
You can find the required trigonometric functions
on any scientific calculator. On many calculators
you access the arccosine function by pressing the
Inverse or second function key and then pressing
the cosine key.
Inverse
Specify Degrees
In Windows you can access a calculator, pictured
here, by clicking on Start–> Programs –>
Accessories –> Calculator. The illustration
highlights the trigonometric function keys and the
Inverse check box. Note that for the formula
giver here you need to specify angular
measurements in degrees, so you should click in
the Degrees option box.
The map depicts Philadelphia and San Francisco.
The following table displays the latitude and
longitude of each place. Use the data in the table
to calculate the numbers of degrees of great circle
arc between the two places and then convert the
degrees into miles.
Here are the steps you need to follow:
1.
2.
3.
Trigonometric functions
Windows calculator. Access by:
Start Programs Accessories Calculator
Convert the degrees, minutes,
and seconds to decimal
degrees.
Use the formula to determine the number of degrees of great circle arc separating the two places.
Multiply the number of degrees by the length of a degree in linear measure [69 in the case of
miles].
Intro to Mapping and GIS F05 Exercise 4
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Global Coordinates
Place
Longitude
Philadelphia
San Francisco
Latitude
75̊ 18' 13" W
40̊ 3' 4" N
121̊ 42' 53" W
36̊ 26' 7" N
Decimal Degrees
Place
Longitude
Latitude
Philadelphia
San Francisco
Sine Lat1 =
Sine Lat2 =
Cos Lat1 =
Cos Lat2 =
Cos (| Long1 - Long2|) =
((Sine Lat1) * (Sine Lat2)) + (Cos Lat1 * Cos Lat2 * Cos (| Long1 - Long2 |) ) =
Arccos of result in previous line.
Degrees
=
degrees.
Distance
=
Miles
Show your work:
Intro to Mapping and GIS F05 Exercise 4
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6 - World Time Zones Worksheet (use page 27 Dates and Times to help you answer)
* Where is all time measured from?
________________________________________
* How many world time zones are there? Why?
________________________________________
* Approximately how wide is each time zone?
________________________________________
* Explain why time zone boundaries are not completely straight.
________________________________________
* Name the four major United States time zones.
________________________________________
If the time in London is 12:00 P.M. GMT, Wednesday what time is it in:
Chicago _____________________________ Paris _____________________________
Moscow _____________________________ Tokyo ___________________________
Buenos Aires ________________________
If the time in Philadelphia is 12:15 P.M., Wednesday what time is it in:
Chicago ____________________________ Paris ______________________________
Moscow ___________________________ Tokyo _____________________________
Sydney ____________________________ Buenos Aires ________________________
Show your work:
Intro to Mapping and GIS F05 Exercise 4
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