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 figure below. North Pole A north latitude Equator A south latitude South Pole 1
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 figure 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. 2
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 figure below.. 30 N 20 N 10 N 0 10 S 20 S. The figure 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 3
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 Position is given as 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) 4
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 figure (i) below. But the information that is suffi cient to calculate the required distance is contained in figure (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 difference between 59 and 25. The total length of the longitude is π (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 π (3960) 34 180 miles 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 figure, and the angle facing the segment AB is z degrees then the distance between the two points is Exercise 1 π (3960) z 180 miles. 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. It is obtained by dividing one degree into 60 equal units. Thus one minute is 1 60th of a degree. We use the 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 35. 5
An even smaller unit is obtained by dividing a minute into 60 equal units. Each one is called a second. Thus one second is 1 60 th of a minute. It follows that one second is 1 3600th of a degree. We use the symbol 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 35 23. We may write such angles in decimal notation by converting minutes and seconds into decimal degrees. For example, 45 is equal to 45 60 = 0.75 degrees, 38 48 is equal to (38 + 48 60 = 38 + 0. 8) = 38.8 141 30 18 = ( 141 + 30 60 + ) 18 3600 = 141.505, 40 35 = ( 40 + 3600) 35 = 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 1 equals 60 seconds to convert the resulting decimal part of the minutes into seconds then round off. 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 44 7 Exercise 1. Convert the given angle measure into a decimal degree: (a) 12 15 36 (b) 95 35 24 (c) 320 5 45 (d) 0 28 48 2. Convert the given angle measure into degrees, minutes and seconds: (a) 36.48 (b) 174.78 (c) 0.0388 (d) 343.45 6