### Trigonometry and The GPS System

```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.
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Positioning System
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
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
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 20 000 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.
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