In simple terms, trigonometry is the ratio of lengths, angles, and triangles. Originating in ancient Greece, trigonometry is an amalgamation of two words, ‘trigono’ meaning triangle, and ‘metry’ meaning measure. If we remember correctly, the problems under this section in our Math books included situations like a shadow of a lamppost falling on the road, tying a rope to a pole, measuring the height of a building, etc.
So, can we use it in our daily life also? Yes, we can and we do also. This is what we will talk about today- how do we use trigonometry in real life?
Trigonometry uses in real life
1. In playing video games
While designing video games, the developers use trigonometry in various aspects. In every game, there are objects that move. The speed and positions of these objects are written using x and y. To find the value of x and y, triangles are formed using the radius and number of degrees the object will move. Using the ‘x’ and ‘y’ values, the objects can rotate in the game also. The popular video game Mario is a fine example.
2. NASA uses it too!
Yes, they use trigonometry to calculate how far a planet or a star is from Earth. For example, to calculate the distance between the Earth and the moon, the circumference of the moon and one of the diameters are used to calculate the arc-length formula. Putting the values, the exact distance in the Miles unit comes out. Neil Armstrong and Edwin Aldrin successfully etched their name in history by landing on the moon only because trigonometry helped in all the calculations.
3. In measuring heights
Everyone knows that Everest has a height of 8848 meters. Indeed, nobody actually climbed Everest with a measuring tape and recorded its height. It is only a trick of trigonometry where a point of observation is located first. Next, you measure the object’s distance from the observation point and the angle between an imaginary line from the top of the object and the observation point. Calculating them with the tan function will give you the height.
4. Developing sound effects
Imagine you are watching a horror movie. When a spirit suddenly appears on the screen, you jump because of the scene and the eerie sound. Also, when you scroll through YouTube, you will find posts like “music for deep concentration, the study” or something like that. How do you think sound engineers develop these sound effects with the perfect pitch, volume, and other things? Yes, you got it right. They study the sound waves created by sine and cosine curves, analyze and comprehend the music and make necessary changes.
5. Building a house? Trigonometry is there to save you!
The construction industry uses trigonometry widely. From measuring how much the roof will be inclined to planning and constructing parallel/perpendicular walls- architects or designers need to calculate all in trigonometry. They use the tan function to decide how long a wall should be. The Sine function helps them measure how far up a wall is. With the exact intersection angles available, architects plan accordingly to ensure the safety of the building.
6. Flying somewhere? Don’t forget trigonometry!
Once an airplane is up in the sky, it is not the engine or the pilot’s skill that keeps it floating. The direction and pressure of wind are also integral to ensuring the safety of the bird. If we take a right-angled triangle and consider the two perpendicular sides, we can get the direction the wind is blowing in. Air Traffic Control uses the speed and angle of flying of the airplane and the speed of the wind. On paper, these data will produce a triangle and calculate the third side using trigonometric ratios. This way, the control tower guides the pilots on which way to use so that the wind direction can facilitate the plane’s journey.
7. Do you hope to be an archaeologist someday? You will need trigonometry!
When you see an excavation site, you will see that the area is not dug up randomly. The archeologists divide the area into equal parts. Where to dig and how deep to dig- these are calculated by trigonometry only. Archaeologists label and mark rock layers into numbered plots to identify which artifact was in which province, calculate the underground position of an artifact from above the ground using their position as the observation point and angle between the artifact and observation point surface, etc. So, to excavate successfully and add to the natural history of humankind, you will find the use of trigonometry.
8. Use trigonometry in navigation
Roughly, navigation is studying any moving object. This can be in four forms: maritime, aviation, terrestrial, and space. We already told you about aviation and space. Sailors at sea use sextant tools and compasses to measure the angle of the sun with the horizon at a particular time. The third angle can be easily calculated considering the vessel as another side of a triangle. GPS, or Global Positioning System, uses triangular trigonometric techniques while orbiting over specific locations on earth. Three positions of the satellites with the earth’s location form a triangle. You can determine where exactly a moving vehicle is using the formula and ratio of trigonometry.
9. Want to explore life underwater? Use trigonometry
Marine biology, or the study of plants and animals inhabiting the ocean, also uses trigonometry. A marine biologist calculates the depression or elevation angle using the water level to understand how far a particular plant or animal is. Also, you find out that there are different types of phytoplanktons or algae at different depths of the ocean. So, the sunlight reaches these algae at different angles too. The length and depth of the sunlight might impact their photosynthesis effectiveness or speed. You can find the answer by connecting the algae’s position, depth of the algae from the sea surface, and angle of sunlight.
10. Manufacturing a car or a shirt- trigonometry finds its use.
Engineers in the automobile industry manufacture vehicles with utmost perfection by accurately calculating trigonometric formulas to estimate the size of the items. These, in turn, ensure that when the car is ready to run on the road, its parts work in absolute coordination. When you go to the tailor and give your measurements for a dress, they tell you to extend your arm. So, your arm and your body create a right angle. Measuring the arm’s length and the length of your torso, they get two sides of a triangle. With the value of the right angle known, they can easily decide the height of the dress. So, whatever there is to manufacture from scratch, trigonometry has extended helping hands.
11. Can you find a Smooth Criminal? Trigonometry will help you!
Forensic specialists or crime investigators study how the blood has spattered; if there is a gunshot hole, they analyze it to understand the angle of impact, etc. Together with this, they use navigation technology. For example, suppose there is a blood droplet a few feet away from the blood splatter. They measure the distance first. Now, they determine the angle of blood impact. The analyst uses these two measurements to form a triangular structure and, using trigonometric formula and tan function, determine the height at which blood has originated. Finally, the criminal’s position and type of weapon are deduced.
12. Trigonometry is your companion in designing a marine ramp
When a marine vessel is floating toward its destination, it needs a proper marine ramp. Using trigonometry, you connect the lower and the higher level areas by forming a sloping surface. This is necessary for building a marine vessel or navigating it.
13. Use in medical service
Many people across the globe continue their everyday life with prosthetic body parts after any accident. Trigonometry helps medical professionals design those based on specific proportions. They measure the angle at which the prosthetic limb should be set to provide stability. Next, they measure the prosthetic limb’s angles while swinging in the air and touching the ground. With these three angles known, they calculate the length and other data of the limb and prepare it accordingly so that it fits perfectly. The suspension system they use for controlled coordination of the amputee’s limbs measures the body as one side of the triangle forming a right angle with the system.
14. Other uses of trigonometry in real life
- Calculating projectile motion, vector components, field strengths, etc. in Physics
- Creating maps or cartography
- Calculating heights of ocean tides in oceanography
- In-depth analysis of sound and light waves through sine and cosine functions
- Satellite design and launch
How can budding learners learn trigonometry?
A few exciting and fun ways to learn trigonometry can be:
- Play a game of building an imaginary tree house. Now try to calculate how tall the tree trunk is.
- Use rhymes with a mathematical twist. For example, use “the mouse ran up the clock” to plot a height graph about how high the mouse will climb every time the clock strikes.
- Use a paper cylinder with an ink blot point. Roll it on a sheet of paper. Now use it as an example of a unit circle.
So, trigonometry has a lot to do in real life apart from only calculating heights, right? Knowing trigonometry deeply means knowing how to solve many a problem. Once you know the formulas and functions by heart, it is nothing to be afraid of. As you can see, trigonometry can be of help in a variety of professions also. So whatever you aspire to be, a mathematician or a seamstress, trigonometry will always accompany you in your career and profession.