Latitudes and Longitudes
Angles are used to label latitudes and longitudes in order to locate points on our planet. It is a known fact
that the earth is approximately a big sphere with a radius that is approximately 3960 miles. The top-most
point of this big sphere is called the north pole. At the opposite end is the south pole. The circle which
divides the earth into two hemispheres, a northern hemisphere and a southern hemisphere, is called the
equator.
North Pole
Equator
South Pole
The latitudes are the circles that are parallel to the equator. A sample of them are drawn on the …gure
below.
North Pole
A north latitude
Equator
A south latitude
South Pole
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Those that are above the equator will be referred to as North latitudes. The South are below the equator.
The longitudes are semi-circles that run from the north pole to the south pole. A sample of them are
drawn in the …gure below.
The longitude that passes through the Royal Observatory in Greenwich, London is called the prime meridian.
Numbering the Longitudes and Latitudes
The equator is called the 0 latitude and the prime meridian is called the 0 longitude. We show you how
the 20 N latitude, the 20 S latitude and the 10 W longitude are obtained. You will then be able to deduce
how all the others are numbered. To construct the 20 N latitude, start by drawing a ray CP from the center
C of the earth to a point P on the equator. Next, draw a ray CQ, also from the center C, to a point Q
which is on the longitude that passes through P and is such that angle QP C is 20 . The circle that passes
through Q and is parallel to the equator is the 20 N latitude.
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To construct the 20 S latitude, draw an angle of
20 instead. The result is shown below.
Note that it is called the 20 S latitude, NOT the 20 latitude. The construction of other latitudes should
be clear. A sample of them is shown in the …gure below.
.
30° N
20° N
10° N
0°
10° S
20° S
.
The …gure below shows the 0 longitude and the 10 West longitude, written as 10 W. The construction
of the 10 W longitude should be self-explanatory. It should also be clear how to construct the 10 East
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longitude, denoted by 10 E:
Other longitudes are constructed in the same way.
To specify the position of a point on the planet, one gives its latitude and its longitude. For example, the
latitude for Riyad in Saudi Arabia approximately 25 North and its longitude is approximately 45 East.
Therefore its position would be given as 25 N, 45 E. Use the globe to complete the following table:
City
Latitude
Longitude
Mombasa, (in Kenya)
Bogota, (in Colombia)
Los Angeles, (in the USA)
Ottawa, (in Canada)
Fairbanks, (in Alaska)
Hong Kong, (in China)
Darwin, (in Australia)
Cape Town, (in South Africa)
Enugu, (in Nigeria)
Atlanta, (in the USA)
Acapulco, (in Mexico)
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Position is given as
Distance Between Points On The Same Longitude
We can easily calculate distances between two points on the same longitude by using direct proportion. For
an example, consider two towns A and B on the same longitude with latitudes 25 N and 59 N respectively.
What is the distance between them?
We may represent the given information by …gure (i) below. But the information that is su¢ cient to
calculate the required distance is contained in …gure (ii). It shows the longitude running from the north pole
to the south pole and the segment of the longitude that is between the two cities. The number 3960 is the
Figure (i)
Figure (ii)
radius of the earth and 34 is the di¤erence between 59 and 25 . The total length of the longitude is
(3960) miles, (i.e. half the circumference of a circle with radius 3960 miles). Note that the longitude is
opposite an angle of 180 and the segment whose length has to be calculated is opposite an angle of 34 . By
direct proportionality, the length of the segment must be
(3960)
34
miles
180
To the nearest mile, this is equal to 2350 miles.
In general, if two given points A and B are on the same longitude, as shown on the …gure, and the angle
facing the segment AB is z degrees then the distance between the two points is
(3960) z
miles.
180
Exercise 1
1. To a good approximation, Gao in Mali and Edinburgh in The United Kingdom are on the same 0
longitude. Locate them on the globe then determine their latitudes and estimate the distance between
them.
2. To a good approximation, Arica in Peru and Ottawa in Canada are on the same 71 W longitude.
Locate them on the globe then determine their latitudes and estimate the distance between them.
Smaller units of angles
There are situations in which angles that are smaller than 1 have to be used. A minute is one such unit.
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It is obtained by dividing one degree into 60 equal units. Thus one minute is 60
th of a degree. We use the
0
0
symbol to denote a minute. For example, 35 minutes are written as 35 and an angle of 40 degrees and 35
minutes is written as 40 350 .
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An even smaller unit is obtained by dividing a minute into 60 equal units. Each one is called a second.
1
1
Thus one second is 60
th of a minute. It follows that one second is 3600
th of a degree. We use the symbol 00
00
to denote seconds. Therefore an angle of 23 seconds is written as 23 , and an angle of 40 degrees, 35 minutes
and 23 seconds is written as 40 350 2300 . We may write such angles in decimal notation by converting minutes
and seconds into decimal degrees. For example,
450 is equal to
45
60
= 0:75 degrees,
141 300 1800 = 141 +
30
60
+
18
3600
38 480 is equal to (38 +
48
60
= 38 + 0: 8) = 38:8
40 3500 = 40 +
= 141:505 ;
35
3600
= 40:0097 , to 4 dec. pl.
In some cases, you may be required to convert an angle in decimal form into an angle in degrees, minutes
and seconds. Simply use the fact that 1 equals 60 seconds to convert the decimal part of degrees into
minutes. After that, use the fact that 10 equals 60 seconds to convert the resulting decimal part of the
minutes into seconds then round o¤. For example, to convert 69:7354 into degree minutes and seconds,
we leave the 69 and convert the decimal part 0:7354 into minutes. The result is 0:7354 60 = 44:124
minutes. We then leave the 44 minutes and convert the decimal part 0:124 minutes into seconds. The result
is 0:124 60 = 7:44 seconds. Therefore, to the nearest second,
69:7354 = 69 440 700
Exercise
1. Convert the given angle measure into a decimal degree:
(a) 12 150 3600
(b) 95 350 2400
(c) 320 50 4500
(d) 0 280 4800
2. Convert the given angle measure into degrees, minutes and seconds:
(a) 36.48
(b) 174.78
(c) 0.0388
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(d) 343.45