Trigonometry is used in many fields including astronomy, architecture, navigation, chemistry, meteorology, engineering, carpentry, biology, and forensics. It allows measurement of distances to stars, calculation of angles and forces in building design, navigation on land and sea, modeling molecular structures, tracking weather balloons, structural design, angled cuts in carpentry, determining molecular structures through x-ray crystallography, and analyzing crime scenes. Trigonometric functions like sine, cosine, and tangent are essential mathematical tools across diverse applications in science and technology.

1. Dharmik Bhatt(17) Jay Patel (28) Aman Juneja(14) Harsh Kahar(20)

2. Trigonometry in Astronomy
• Measuring distances to objects within our Galaxy is not
always a straightforward task – we cannot simply stretch
out a measuring tape between two objects and read off
the distance. Instead, a number of techniques have been
developed that enable us to measure distances
to stars without needing to leave the Solar System. One
such method is trigonometric parallax, which depends on
the apparent motion of nearby stars compared to more
distant stars, using observations made six months apart.

3. Trigonometry in Architecture
• Mathematics makes the design of buildings safer and more
accurate. Trigonometry is especially important in architecture
because it allows the architect to calculate distances and
forces related to diagonal elements. Of the six functions in
basic trigonometry, the sine, cosine and tangent are the most
important to architecture because they allow the architect to
easily find the opposite and adjacent values related to an
angle or hypotenuse, translating a diagonal vector into
horizontal and vertical vectors.

4. Trigonometry in Navigation
• Trigonometry also plays a part in navigation. It assists with the
calculation of the coordinates of a specific point on a
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. Trigonometry is also used to navigate from one
place to another on a straight line. This can therefore also tell
you the distance from you, to your destination.

5. Trigonometry in Chemistry
• Chemists use trigonometric functions to accurately describe
the angles that are created when atoms bond together to
form molecules. chemists can represent the shape of the
molecule most accurately in a three-dimensional model,
which can be obtained using trigonometric functions. The
molecule is represented within a triangular prism so that
chemists can work out the equations that determine the
interior angles and length of the triangle's three sides, which
are called the opposite, adjacent and hypotenuse

6. Trigonometry in Meteorology
• Meteorology is the scientific study of the atmosphere. A
meteorologist uses trigonometry for analysis, modelling and
prediction. Weather balloons are used to help measure
temperature, humidity and wind. These balloons can typically
ascend to 100,000 feet and drift for 125 miles. They carry a
device called a radiosonde, which takes humidity, pressure
and temperature measurements. The initial height of the
balloon can be calculated from the tangent function with the
use of a ground crew’s distance and angle of sight. The
tangent function is also used to calculate the balloon’s height
when it's between two observation stations. The balloon’s
height, angle, distance and travel time can be used in
calculations to help estimate wind speed.

7. Trigonometry in Engineering
• Trigonometry is not just a subject to be studied in a classroom
with no real world practical applications. Engineers of various
types use the fundamentals of trigonometry to build
structures/systems, design bridges and solve scientific
problems. When all of the measurements of the structure are
known the engineer can begin building and defining the scope
of the project they are undertaking.

8. Trigonometry in Carpentry
• Carpentry calls for trigonometry more than you might think.
Every time a carpenter makes an angled cut, the
measurement of the angle or the adjoining lines must be
figured out. Trigonometry is used in many other carpentry
applications, including site layout tasks that require using
angular measurements. These tasks might include laying out
building foundation lines and determining elevations by
completing trigonometric levelling.

9. Trigonometry in Biology
• Trigonometry comes up in many aspects of biology. One example is
X-ray crystallography, a technique used to determine the three
dimensional structure of molecules. X-ray crystallography has been
used to determine the atomic structure of thousands of biologically
important molecules including vitamins, proteins, and perhaps most
famously DNA. X-ray crystallography exploits the fact that when an
x-ray is passed through a crystal, it is diffracted according the
crystal's atomic structure.

10. Trigonometry in Forensics
• Forensics use trigonometry to analyze crime scenes and collect clues. They
first check for any bullet holes in ceilings, floors and furniture. Next They
try and re-enact the crime scene in order to try and presume what
happened. this is where trigonometry comes in. Trigonometry helps them
to suggest where the suspect or victim was located at the time of the
incident.For example, a bullet fired into a wall, at an angle of 90° can show
the investigators the size of the bullet. This can also help to determine the
specific gun used by the shape of the hole in the wall.If the angle is off by
even the slightest degree, that makes the hole an ellipse. With a hole of
this type, investigators can not only determine the size of the bullet, but,
by using basic trigonometry, they can tell where the bullet came from.

11. So Maths is not always boring.