What Are Some Real-Life Applications of Trigonometry?

By Emily Beach
A close-up of the Bay Bridge in San Francisco.

Trigonometry, the branch of mathematics that describes the relationship between the angles and lengths of triangles, was originally developed thousands of years ago as a way to calculate distances, allowing people to plot the stars and navigate the seas. Since then, the applications have expanded dramatically. It can seem like trigonometry is never used outside of the classroom, but you may be surprised to learn just how often applications of trigonometry are encountered in the real world.



Architecture and Engineering

Much of architecture and engineering relies on triangular supports. When you drive across a suspension bridge, you are benefiting from trigonometry, which an engineer used to calculate the correct length of support cables, the height of support towers, and the angle between the two. Trigonometry also allows builders to correctly lay out a curved wall, determine the proper slope of a roof or the proper height and rise of a stairway. You can even use trigonometry in more casual building-related applications on your personal property. You can determine the height of a tree on your property without the need to climb dozens of feet in the air, or find the square footage of a curved piece of land.

Music

Trigonometry plays a major role in musical theory and production. Sound waves travel in a repeating wave pattern, which can be represented graphically by sine and cosine functions. A single note can be modeled on a sine curve, and a chord can be modeled with multiple sine curves used in conjunction with one another. A graphical representation of music allows computers to create and understand sounds. It also allows sound engineers to visualize sound waves so that they can adjust volume, pitch and other elements to create the desired sound. Trigonometry plays an important role in speaker placement as well, since the angles of sound waves hitting our ears can influence the quality of the sound.

Electricity

Modern power companies use alternating current to send electricity over long-distance wires. In an alternating current, the electrical charge regularly reverses direction to deliver power safely and reliably to homes and businesses. Electrical engineers use trigonometry to model this flow and change of direction, with the sine function used to model voltage. Every time you flip on a light switch or turn on the television, you’re benefiting from the application of trigonometry.

Industry

Trigonometry plays a major role in industry, where it allows manufacturers to create everything from automobiles to high fashion. Engineers rely on trigonometric relationships to determine the sizes and angles of mechanical parts used in machinery, tools and equipment. This math plays a major role in automotive engineering, allowing car companies to size each part correctly and ensure they work safely together. Even determining the angle of darts or length of fabric needed to craft a certain shape of skirt or shirt can be accomplished using basic trigonometric relationships.

About the Author

Emily Beach works in the commercial construction industry in Maryland. She received her LEED accreditation from the U.S. Green Building Council in 2008 and is in the process of working towards an Architectural Hardware Consultant certification from the Door and Hardware Institute. She received a bachelor's degree in economics and management from Goucher College in Towson, Maryland.