Some Applications of Trigonometry Revision Notes

Trigonometry simply deals with calculations of triangles (that’s where the tri comes from). It is a study of relationships in arithmetics involving lengths, heights, and angles of different triangles. Trigonometry is a discrete subject than most of the maths we have encountered in our lives previously. Applications of trigonometry are spread across different fields like astronomy, engineering, architecture, physics, crime scene investigation, etc.

Trigonometry Basics

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Some basic concepts of trigonometry that need to be understood before looking at its applications are:

• Line of Sight - It is the line from the eye of the observer to the point on the object that is viewed. 
• Horizontal level is the horizontal line drawn through the eye of the observer.
• The angle of elevation - It is relevant for objects that are above the horizontal level. It is the angle that is formed by the horizontal level line with the line to the object above the horizontal level.
• The angle of depression is mainly related to objects that are below the horizontal level. It is the angle that is formed by the line of sight with the line to the object below the horizontal level.

Applications of trigonometry

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The real-life applications of trigonometry are:

• It helps in measuring the separation/distance of Celestial bodies: Large distances can be measured by the use of the parallax method. The parallax angle is half the angle between two lines of sight when an object is viewed from two different positions. If we know the angle of the parallax and the distance between the positions, then distance could be measured using trigonometry.
• It helps in measuring length while constructing buildings and towns: The dimensions of the building that is to be constructed or designed are calculated by the use of trigonometry only.
• It helps in calculating heights and distances.
• It helps in calculating the height of tidal waves in oceans within oceanography.
• The sine and cosine functions are generally used in determining the sound and light waves.
• Trigonometry and Algebra together form calculus.
• It helps in the cartography - creation of maps.
• Trigonometry is used in developing computer music in the form of sound waves.
• It helps in measuring the length of mountains, rivers, etc. 
• It is used in satellite systems.

Trigonometry Uses in Different Industries

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• Trigonometry in Aviation

• In the aviation industry, trigonometry is used to keep a check on the direction, distance, and speed of the wind as well as plane. 
• The direction of the wind is very important in this field for pilots to fly a plane.

• Trigonometry in Criminology

• When someone needs to investigate a crime scene, they use trigonometry. 
• The trajectory or path of the projectile could also be determined with the help of trigonometric ratios. 
• It is also used in determining the phenomenon of a falling object with a particular angle.

• Trigonometry in Marine Biology

• Marine biologists often take the help of trigonometry to figure out the depth of sunlight that is affecting the growth of algae for photosynthesis. 
• They try to estimate the size of other animals like sharks, whales and study their behavior so algae are not impacted.

• Trigonometry in Navigation

• It is used for estimating and navigating the directions to make the placement of the compass easier in order to get a straight direction. 
• It is easier to pinpoint using a compass and trigonometric functions for finding the distance to see the horizon.

• Trigonometry in video games:

• In many games like Mario, a character is smoothly gliding over the surface in a parabolic/curved path defending the blocks/hurdles in its pathway rather than jumping straight along the y-axis.
• Trigonometry helps Mario jump over these obstacles. Trigonometry is also an important aspect for these engineers in the gaming industry.

• Trigonometry in construction:

• We need trigonometry In construction for measuring fields, lots, and areas; making walls parallel and perpendicular; installing ceramic tiles; roof inclination; determining the height of the building, the width, length, etc.

• Trigonometry in marine engineering:

• Trigonometry is used in marine engineering to build and navigate marine vessels. 
• Trigonometry is used for designing marine ramps which connect the higher and lower level through a sloping surface/staircase according to the need and application.

• Trigonometry in physics:

• Trigonometry In physics is used to find dot and cross products and other components of vectors. 
• It is also used for electromagnetic waves and for understanding the mechanisms of models of waves and oscillations. 
• We use trigonometry for the calculation and determination of projectile motion also.

• Trigonometry for archaeologists 

• Archaeologists divide the excavation site with the help of trigonometry into equal parts maintaining symmetry. 
• They need to identify different tools for their work. Archaeologists also measure the underground water and tank systems.