How to Use Trigonometry in Architecture

By Kevin Lee; Updated April 24, 2017
High-tech tools and simple trigonometry help architects work effectively.

Ancient architects had to be mathematicians because architecture was part of mathematics. Using math and design principles, they built pyramids and other structures that stand today. Because angles are an intricate part of nature, sines, cosines and tangents are a few of the trigonometry functions ancient and modern architects use in their work. Surveyors also use trigonometry to examine land and determine its boundaries and size. Although surveyors perform this task, architects may rely on surveys when designing structures.

Gleaning Important Information From Triangles

One of the most common architectural uses for trigonometry is determining a structure's height. For example, architects can use the tangent function to compute a building's height if they know their distance from the structure and the angle between their eyes and the building's top; clinometers can help you measure those angles. These are old devices, but newer ones use digital technology to provide more accurate readings. You can also compute a structure's distance if you know a clinometer angle and the structure's height.

Basic Structural Theory

In addition to designing the way a structure looks, architects must understand forces and loads that act upon those structures. Vectors -- which have a starting point, magnitude and direction -- enable you to define those forces and loads. An architect can use trigonometric functions to work with vectors and compute loads and forces. For instance, you can use sine and cosine functions determine a vector's components if you express it terms of the angle it forms relative to an axis.

Truss Analysis and Trigonometry

Designing structures that can handle load forces applied to them is important for architects. They often use trusses in their design to transfer a structure's load forces to some form of support. A truss is like a beam but lighter and more efficient. You can use trigonometry and vectors to calculate forces that are at work in trusses. An architect may need to determine stresses at all points in a truss with its diagonal members at a certain angle and known loads attached to different parts of it.

Modern Architects and Technology

Examine a modern city's skyline and you'll probably see a variety of aesthetically pleasing and sometimes unusual buildings. In addition to trigonometry, architects use calculus, geometry and other forms of math to design their creations. Structures not only have to be sound but also must satisfy building regulations. Armed with high-speed computers and sophisticated computer-aided design tools, modern architects harness the full power of mathematics. Unlike ancient architectural wizards, today's architects can create virtual models of projects and tweak them as necessary to create fascinating structures that command attention.

About the Author

After majoring in physics, Kevin Lee began writing professionally in 1989 when, as a software developer, he also created technical articles for the Johnson Space Center. Today this urban Texas cowboy continues to crank out high-quality software as well as non-technical articles covering a multitude of diverse topics ranging from gaming to current affairs.