Trigonometry has a lot of real-life applications, such as in astronomy, where it is used to calculate the distance between planets and stars. Other than that, one application of trigonometry is the calculation of the height and distance of various objects in the real world.
Before understanding the application of trigonometry, we need to understand some basic terms, such as
1. Line of Sight
Consider a person looking at the top of the light tower, as in the figure: the line drawn from the eye of the boy to the top of the tower is called a Line of Sight.
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2. Angle of Elevation
Consider a person looking at the top of the light tower as in the below figure.
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The angle between the line of sight and the horizontal level at the eye of the boy, ΔCDA or ∠D, is called the angle of elevation.
When we measure the angle of elevation, the observer should raise their head and look above the horizontal level.
Here, if one wants to calculate the height of the tower without actually measuring it, then what and how much information is required?
The following detail is necessary to find out the height of the tower without measuring it:
- Distance, AB or CD, between the tower and the point where the boy is standing.
- The angle of elevation, ∠EDC, of the top of the tower.
- The height of the boy DA.
In ΔCDE, the known ∠D is the opposite of the side CE, and CD. So here is the trigonometry ratio that can be used to apply all these three quantities. Determine tan D or cot D as their ratio involves CD and CE.
3. Angle of Depression
Now consider a situation as in the given figure 4: a person is looking towards a ball from a balcony. Its line of sight is below the horizontal level. The angle between the line of sight and the horizontal level is called the angle of depression.
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Thus, the angle of depression of the point on the object is the angle between the horizontal level and line of sight when the point is below the horizontal level.
In the above figure, the person at point C is looking towards the ball at B. CB is the line of sight, and AC is the height of the balcony.
In ΔBCD, ∠BCD is the angle of depression of point B. Here is the height of the balcony AC = BD and the distance of the ball from the ground foot of the building AB = CD. According to the given data, the trigonometry ratio can be used, as it can involve both known and unknown quantities.
Real-Life Applications
There are various applications of trigonometry, and some of the common applications of trigonometry are the following:
Trigonometry to Measure Height
The basic use or application of trigonometry is the measure of height. We use the concept of trigonometry to measure the height and distance between two objects by measuring the angles between these objects.
We can easily find the height of an object if we know the distance between any point and the foot of the building and the angle of elevation or the depression of that point from the building.
Trigonometry in Aviation
We use trigonometry in aviation for measuring the height and speed of any flying objects such as Airplanes and missiles.
The exact position of the airplane and other flying objects can be measured if we are given its height and the angle of elevation.
Trigonometry in Navigation
Trigonometry is widely used in the navigation of ships, and others can easily find the position of our ship in the ocean with the help of stars and the knowledge of trigonometry and angles.
Trigonometry in Astronomy
Trigonometry is widely used in astronomy to find the distances and positions of the stars and other heavenly bodies.
We can measure the angle of various heavenly bodies from the Earth by knowing the time taken by the light from that body to reach the Earth's surface and the speed of light; we can find its position in space using trigonometry.
Other Uses of Trigonometry
The other uses of trigonometry are discussed below.
- It is used in criminology to study crime scenes, such as determining the path of bullets or crime scene reconstruction.
- It is used by marine biologists to study the depth of oceans using echo sounding or triangulation.
- It is used to study waves and their properties, as waves in mathematics can be represented using sine or cosine functions.
