Back ground about the trigonometry  1) Trigonometry means: measuring with triangles.  2) This word came from different languages as other scientific words that usually came from( Arabic, Latin, Greek, and Indian).  3) In the Greek language the plane figure with straight line is called polygon, so the three sided figure will be Trigon as they use the prefixes like( tetra, penta, hexa,..etc)

 4) In the Latin language it is the triangle that means the three-corners shape.  5) Finally we have triangulation from Latin and trigonometry from Greek.

Main Ideas about The Global Positioning System  1) It is a system that was originally developed by the United States for military use, and they tried to stop the people from using it at the beginning but finally they gave up and now every one is using it for free.  2) This system is build up on the trigonometry.  3) The ancient people were using trundle wheel or a real tape measure, and that was for the small distances without having mountains or rivers. So The main benefit of this system is to make the calculation of the distances easier and more quicker as we are in the 21 Century.

 4)In our days all that we need to do is to have a GPS receiver in order to calculate our position and its distance from another location.  5)The GPS consists of twenty four GPS Satellites each orbiting the earth twice a day at a height of about km

The relationship between Trignometry and the GPS - The mechanism of the action: *The significance of the time: Each of the GPS satellites and every GPS receiver contains a clock, and all of these clocks are set to exactly the same time. Each GPS satellite broadcasts this time continuously, and also an almanac, saying exactly where it is supposed to be at that time. This signal travels at the speed of light, which means that by the time it reaches the GPS receiver there will be a difference between this time and the time given by the clock inside the receiver. By that difference we can calculate the distance between the GPS satellite and the GPS receiver to an accuracy of less than a meter!

* The requirement for the process: is to receive signals from at least three satellites. * The role of the trigonometry in the process: When we receive the signals the shape that we get it is mainly based on triangles, so that we can use the trigonometry rules when we have the distance from one spot to another for example; The sine and the cosine. Etc.

CONCLUSION  1) As every thing in the world related to the sciences, the GPS system related to the sciences; which means that the GPS doesn’t replace the trigonometry but it is one of the needs that people want it in our day.  2) The GPS is used in countless field in our life: Airplanes, cars, smart phones, military targets, blind people.

A related video that explains how the GPS works.  MkFsJXRI MkFsJXRI