When Will I Use Trigonometry in Real Life? Practical Applications Explained

If you've ever sat in a math class wondering, "When will I actually use trigonometry in real life?", you're not alone. Trigonometry may initially seem abstract, even boring, with its sines, cosines, and tangents, but it's truly quite crucial in the real world.

In this article, we'll explore the practical applications of trigonometry, examine real-life applications in different fields, and explain why trigonometry is much more than just a school subject.

Before discussing real-world applications of trigonometry, it is important to understand what trigonometry really is. Well, in simple terms, trigonometry is the study of the relationships between the angles and sides of triangles, especially right triangles. At its core, it is about measuring and relating distances and angles. Formulas like sine (sin), cosine (cosine), and tangent (tan) may feel abstract, but you'll soon see how they help us solve practical problems involving height, distance, motion, waves, and more.

First, you need to know (or remember) that there are three basic functions of trigonometry: sine (sin), cosine (cos), and tangent (tan). These three basic functions are used to derive other critical trigonometric functions: cotangent (cot), secant (sec), and cosecant (csc).

Suppose you have $\theta$, the angle in a right triangle formed between (BC) and (AC), then:

The value of cot, sec, and cosec depends on tan, cos, and sin, respectively:

Now that you know the basics of trigonometry, you're all set to learn more about real-life applications of trigonometry.

We can use trigonometry to measure the height of a building, mountain, tree, etc. The height can be easily determined by measuring the horizontal distance from the base and the elevation angle to the top.

Example

Suppose you want to calculate a building's height. If the distance between the building and a person and the angle formed when the building is viewed from the ground are known, you can use trigonometry to calculate the height.

Let's assume that you know the angle of elevation ($\theta$) and the distance between the person and the building, the formula that you need is as follows:

The distance is $\mathrm{100 ft}$, and the angle formed is $\mathrm{45°}$, then:

Because $\tan(45°) = 1$, then the height is also equal to $\mathrm{100 ft}$. Check out our tangent calculator 🇺🇸 to simplify trigonometric calculations.

In construction, trigonometry is essential for measuring ground surfaces and land areas before building begins. It is applied in many aspects of structural design, such as:

• Calculating roof inclinations;
• Wall alignments; and
• Angles of light and shadow.

Even practical details, like ensuring the correct placement of ceramic tiles 🇺🇸 or stones, rely on trigonometric principles to achieve precision and balance in construction projects.

Trigonometry also plays a vital role in aviation. For example, for an airplane's path from landing to take-off, it helps calculate the:

• Direction;
• Speed; and
• Slope.

Pilots and engineers rely on it to determine the optimal take-off, landing angles, and speeds. Since wind strongly affects flight performance, trigonometric calculations help establish the precise angle at which the aircraft should land or take off, as well as the safest and most efficient speed for the maneuver.

Trigonometry is also widely used in navigation. With the help of a compass, it provides accurate directions toward a destination. Sailors and navigators apply trigonometric principles to calculate the distance between a point at sea and the shoreline. Similarly, modern satellite navigation systems rely on trigonometric functions, such as the law of cosines 🇺🇸, to solve equations that determine the precise position of satellites in Earth's orbit and, in turn, help locate positions on the ground.

The solar system has fascinated humans around the world since the dawn of civilization. But did you know that trigonometry is used in astronomy?

For example, astronomers use trigonometry to calculate the distance between stars, planets, and other bodies in the solar system relative to Earth. NASA scientists also use it to design and launch space shuttles and rockets.

When you think about it, without trigonometry, there would be no satellites in orbit or human missions to the Moon. Amazing, isn't it?

Marine biologists study ocean life, from plants and animals to other underwater species. To facilitate their research, they often use trigonometry to estimate the distance and angle at which a marine organism is located in relation to the observer. Depending on the scientist's position, this may involve an angle of elevation or depression. In this case, the water level is considered the base of a right triangle, while the depth of the organism forms the vertical side, and the line of sight represents the hypotenuse. By applying trigonometric functions, marine biologists can calculate the size of large marine animals and better understand their behavior.

Trigonometry has many other fascinating applications, including:

• Criminology: It is used at crime scenes to determine the estimated cause of a collision in an accident or at what angle a gunshot was fired.
• Waves and physics: Sine and cosine functions describe the behaviour of sound and light waves (check out our wavelength calculator 🇺🇸 to learn more about it).
• Oceanography: Trigonometry helps measure the height of waves and predict tides.
• Cartography and navigation: It is essential in map-making as well as in the naval and aviation industries.
• And many more!

At first glance, trigonometry may seem like nothing more than a series of abstract formulas. But when you take a step back, it's easy to see how deeply rooted it is in our daily lives. Whether it's flying planes, building houses, navigating the oceans, designing maps, or even studying marine creatures, trigonometry helps us understand the world around us in practical and concrete ways.

So, the next time you ask yourself, "When will I ever use trigonometry in real life?", remember that it's already at work all around you.