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July 30, 201239 Insightful Publications

**Real-Life Applications of Trigonometry:** Trigonometry simply means calculations with triangles. It is a study in mathematics that involves the lengths, heights, and angles of different triangles. The field emerged during the 2nd century Before the Common Era (BCE), from applications of geometry to astronomical studies, apart from mathematics, trigonometry has applications in the field of physics. If a student is able to grasp the various concepts of trigonometry in school, they are likely to score better in exams.

Trigonometry formulas have applications in various fields such as construction, design, and other branches of engineering. It is even applied to crime scene investigations. In this article, we have come up with detailed information on different real-life applications of Trigonometry in various fields of our life.

Before going to the details of its applications, let us answer a question:

**Have you ever wondered what field of science first used trigonometry?**

The immediate answer expected would be mathematics but it does not stop there, even physics uses a lot of concepts of trigonometry. According to Morris Kline, in his book named “Mathematical Thought from Ancient to Modern Times”, proclaimed trigonometry was first developed in connection with astronomy, with applications to navigation and construction of calendars.

This was around 2000 years ago. Geometry is much older, and trigonometry is built upon geometry’. However, the origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia, and India more than 4000 years ago. Greek astronomer Hipparchus composed the first trigonometry table in 127 BCE.

Trigonometry may not have its direct applications in solving practical issues, but it is used in various things that we enjoy so much. For example, music. As you know sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music.

A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. This means sound engineers need to know at least the basics of trigonometry. Real-life applications of Trigonometry have helped in the development of everyday human life activities. And the good music that these sound engineers produce is used to calm us from our hectic, stress full life – All thanks to trigonometry.

If you know the distance from where you observe the building and the angle of elevation you can easily find the height of the building. Similarly, if you have the value of one side and the angle of depression from the top of the building you can find and another side in the triangle, all you need to know is one side and angle of the triangle.

Have you ever played the game, Mario? When you see him so smoothly glide over the roadblocks. He does not really jump straight along the Y-axis, it is a slightly curved path or a parabolic path that he takes to tackle the obstacles on his way. Trigonometry helps Mario jump over these obstacles. As you know Gaming industry is all about IT and computers and hence Trigonometry is of equal importance for these engineers.

In construction we need trigonometry to calculate the following:

- Measuring fields, lots, and areas;
- Making walls parallel and perpendicular;
- Installing ceramic tiles;
- Roof inclination;
- The height of the building, the width length, etc., and the many other such things where it becomes necessary to use trigonometry.

Architects use trigonometry to calculate structural load, roof slopes, ground surfaces, and many other aspects, including sun shading and light angles.

Flight engineers have to take into account their speed, distance, and direction along with the speed and direction of the wind. Trigonometry table comes in handy for basic calculations. The wind plays an important role in how and when a plane will arrive where ever needed this is solved using vectors to create a triangle using trigonometry to solve.

For example, if a plane is travelling at 234 mph, 45 degrees N of E, and there is a wind blowing due south at 20 mph. Trigonometry will help to solve for that third side of your triangle which will lead the plane in the right direction, the plane will actually travel with the force of wind added on to its course.

In physics, trigonometry formula is used to find the components of vectors, model the mechanics of waves (both physical and electromagnetic) and oscillations, sum the strength of fields and use dot and cross products. Even in projectile motion, you have a lot of application of trigonometry.

Trigonometry is used to divide up the excavation sites properly into equal areas of work. Archaeologists identify different tools used by the civilisation, and using trigonometry can help them in these excavates. They can also use it to measure the distance from underground water systems.

In criminology, trigonometry can help to calculate a projectile’s trajectory, to estimate what might have caused a collision in a car accident or how did an object fall down from somewhere, or in which angle was a bullet shot, etc.

Marine biologists often use trigonometry formula to establish measurements. For example, to find out how light levels at different depths affect the ability of algae to photosynthesise. Trigonometry is used in finding the distance between celestial bodies. Also, marine biologists utilise mathematical models to measure and understand sea animals and their behaviour. Marine biologists may use trigonometry to determine the size of wild animals from a distance.

In marine engineering, trigonometry is used to build and navigate marine vessels. To be more specific trigonometry is used to design the Marine ramp, which is a sloping surface to connect lower and higher-level areas, it can be a slope or even a staircase depending on its application.

Trigonometry is used to set directions such as the north-south or east-west. It tells you what direction to take with the compass to get in a straight direction. It is used in navigation in order to pinpoint a location. It is also used to find the distance of the shore from a point in the sea. It is also used to see the horizon.

Following are the other real-life applications of Trigonometry:

- It is used in oceanography in calculating the height of tides in oceans.
- The sine and cosine functions are fundamental to the theory of periodic functions, those that describe sound and light waves.
- Calculus is made up of Trigonometry and Algebra.
- Trigonometry can be used to roof a house, to make the roof inclined ( in the case of single individual bungalows) and the height of the roof in buildings, etc.
- It is used in the naval and aviation industries.
- It is used in cartography (creation of maps).
- Also, trigonometry has its applications in satellite systems.

Here are some of the frequently asked questions on real-life applications of trigonometry.

**Q1: What is trigonometry and its applications?Ans:** Trigonometry has got a lot of applications in different areas of life including Engineering, Arts, Music, Games, etc.

**Q2: What are 6 occupations that use trigonometry?Ans:** Six occupations that use trigonometry are:

(i) Marine Engineering

(ii) Game Development

(iii) Construction

(iv) Naval & Aviation

(vi) Criminology

**Q3: Why do we need trigonometry?Ans: **Trigonometry is a very important part of Mathematics that is used in different fields of our life. To name a few, trigonometry formula help in construction, marine navigation and archaeology.

**Q4: Who is the father of trigonometry?Ans: **Hipparchus is considered the father of trigonometry.

**Q5: What are the applications of trigonometry Class 10?Ans: **Trigonometry for Class 10 helps us solve problems related to heights and distances, angle of elevation and depression etc.

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