applications of trigonometry
TRANSCRIPT
AYUSH KUMAR OJHAX A
APPLICATIONS OF TRIGONOMETRY
ABOUT
Trigonometry is part of mathematics that makes relationship between angle and length of a triangle.
It was invented because its need arose in astronomy to calculate distances and angle. And subsequently being used in a number of applications.
Briefly it implies that – In a triangle if at least the length of one side and the value of one angle is known, then all other angles and lengths can be determined algorithmically.
Who Invented ?
The ancient Greeks were the first to develop the conceptual framework of trigonometry. The noted Greek astronomers Hipparchus, Menelaus and Ptolomy contributed in advancing the theory.
Many historians refer to Hipparchus as the father of trigonometry.
PRIMITIVE USE OF TRIGONOMETRY
Trigonometric tables were created over two thousand years ago for computations in astronomy.
The kind of trigonometry needed to understand positions on a sphere is called spherical trigonometry.
TRIGONOMETRY FOR HEIGHT & DISTANCE
One of the most common applications of trigonometry is the use of triangulation to determine the height of buildings, mountains, trees and other very tall or distant objects.
A CASE EXAMPLE
During the survey in 1852, the highest mountain in the world was discovered. From a distance of over 160 km, the peak was observed from six different stations. In 1856, this peak was named after Sir George Everest, who had commissioned and first used the giant theodolites.
How can we use Trigonometry?
Ravi wants to find the height of the tower but he can not climb over to measure it.
40 mtr600
AB
C
• With the help of measuring tape, he moves away 40 m from the base of the tower.
• There he finds angle between top of the tower (line of sight) and the plane as 600 which is called angle of elevation.
How can we use Trigonometry?
40 mtr600
AB
C
• Here we have to find the height AC, where given are the base AB=40 m and <B=60o
• Since, our problem relates to Height and Base only so we will use Tanθ which is the ratio of Height/Base.
• Tan θ = or Tan 60o=
• or AC=40
NAVIGATION AND TRIGONOMETRY
Finding distance of the island without having to measuring it.
It is used in navigation to find the distance of the shore from a point in the sea.
NAVIGATION AND TRIGONOMETRY
It assists with the calculation of the coordinates of a specific point on a map using Cartesian coordinate plane.
This is also used to represent the directions of the four compass points: north, south, east and west, where it is used for finding the bearing of an object from another.
NAVIGATION AND TRIGONOMETRY
A position on the surface of the earth is determined by means of latitude (measure from equator) and longitude, where trigonometry is used to find distances.
SOME MORE APPLICATIONS OF TRIGONOMETRY
ArchitectureMeteorologyEngineeringAcousticsComputer graphicsGame development.
Trigonometry in Technologies
Ships, Aeroplane & RadarGPS Global Positioning System
technology feeds electronic navigation devices with location data. GPS uses some fairly complex calculations, largely based on the trigonometry.
Points to Remember
Ratio of the sides based on angle in a triangle is only the basics of Trigonometry.
The subject is too vast and it is used in other mathematical theories also.
Trigonometry not only deals with Right angle triangle but can also be used for any type of triangle.