Trigonometry was invented by ancient Greeks to calculate distances and angles in astronomy. It relates the angles and lengths of triangles, allowing unknown values to be determined if one angle and one length are known. Some early applications included creating trigonometric tables for astronomical computations and using triangulation to measure heights and distances. Modern uses include navigation, surveying, engineering, acoustics, and technologies like GPS which rely on trigonometric calculations.

1. A Y U S H K U M A R O J H A
X A
APPLICATIONS OF
TRIGONOMETRY

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. How can we use Trigonometry?
 Ravi wants to find the height of the tower
but he can not climb over to measure it.
40 mtr
600
A
B
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.

8. How can we use Trigonometry?
40 mtr
600
A
B
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 =
𝐴𝐶
𝐴𝐵
or Tan 60o=
𝐴𝐶
40
• 3 =
𝐴𝐶
40
or AC=40 3

9. 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.

10. 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.

11. 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.

12. SOME MORE APPLICATIONS OF
TRIGONOMETRY
 Architecture
 Meteorology
 Engineering
 Acoustics
 Computer graphics
 Game development.

13. Trigonometry in Technologies
 Ships, Aeroplane & Radar
 GPS Global Positioning System technology
feeds electronic navigation devices with location
data. GPS uses some fairly complex calculations,
largely based on the trigonometry.

14. 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.