As we have seen, trigonometric functions play an integral part in architectural concepts and theories. They are used to determine angles of lines and shapes, as well as calculating areas and volumes.

Trig is so heavily integrated into architecture that it is difficult to describe all its applications without getting very technical. That is why there are many resources available online with easy ways to apply trigonometry in your career.

This article will go more in depth about how architects use trigonometry for conceptualization and planning.

3D modeling

The most fundamental way tron­gon­metry is used in archi­tec­ture is for three-dimensional (3D) model­ing. This includes creating computer models of buildings, landscapes, or other shapes so that you can then create virtual recreations of them using software such as Adobe Photoshop or SketchUp.

In these programs, you take your uploaded 3D model and manipulate it to achieve different looks – something like making a house look more curvy or boxy depending on what effect you want to go for. Professionals also use tron­gon­mory for figuring out angles and proportions of various architectural features; for example, calculating the height and width of an outside wall or how much roof space there is between two roofs.

There are several online resources where you can learn more about tron­gon­mry and its applications in architecture. But all too often people start off learning the basics and then give up because they feel overwhelmed.

2D drafting

In drawing or diagramming, two dimensional (2D) representations of three-dimensional (3D) shapes and structures are made using trigonometric functions. This is done through geometry or calculus.

Trig is one of those tricky areas that seems to have no clear definition. Some say it’s just math while other experts feel it goes beyond that!

But what most agree on is that trig involves triangles. And there you have it—triangles!

Triangles play an important role in many disciplines. They can be used to understand how things work, how well they work, and even how to improve them.

That’s why knowing your basics of trig is very valuable. Luckily for you, we’ve gathered some helpful information here! So let’s get into it. We'll start with something easy.

Construction mathematics

Another integral part of architecture is construction mathematics, or as it’s more commonly known, geometry. This includes things such as measuring angles, lengths, and areas, among others.

Trigonometry plays an important role in this, as you can probably guess. The trigonometric functions are familiar to most people, so using them when doing these calculations will not pose too much of a challenge.

For example, we would use sine for calculating angle degrees between two lines, cosine for calculating area, and tangent for finding the slope of a line all within reason of the function being used!

These concepts are very crucial in architectural design, especially with respect to proportion. Proportion is determining how close one thing is related to another relative to their size, and knowing trig allows us to do that effectively.

Measurement and precision

In architecture, there are two main types of functions performed using trigonometric formulas. The first is measuring angles, which includes calculating the angle between two lines or planes. This is typically done by finding the difference between the internal and external angles of a triangle that contains both lines or planes.

The other type of function used in architectural design is precise mathematical calculation. These calculations often involve longhand equations, so they may be difficult to do without help. Computers make this kind of work easy!

There are several computer software programs designed for architects to use. Some examples include AutoCAD, SketchUp, and Adobe Photoshop. All of these have powerful built-in tringonometrical functionality that users can access.

These apps usually have some sort of calculator feature as well, which makes doing basic math much easier.

Oblique viewing

With oblique viewing, you can create an angled view of something by including both vertical and horizontal angles in your shot. By incorporating more than one angle, you get an overall feeling that the viewer must invest energy to look at the image fully.

Oblique views are extremely popular in architecture because they give people a sense of mystery. When looking at a building from the side or front, it is difficult to determine what parts have been left out. It makes the setting feel secretive and mysterious.

This effect also creates a feeling of separation between observer and object, which many architects use for inspiration. They take a simple structure and add lots of depth and intrigue.

In this article, we will discuss some applications of trigonometry in architectural drawing.

Right angles

Another fundamental concept in architecture is that of right angle. A right angle occurs when two lines are so close together that they form a smaller, narrower line or shape.

Take a look at the following example.line Ais longer than line B. Because of this, we can describe line B as being “narrower” or having less space beside it than line A.

This does not occur often in nature, but you will find them frequently in mathematics. For instance, there is one inside the Pythagorean theorem!

Theorems like these show that if a triangle has a right angled side then the area of the triangle is determined by the length of the other sides.

Architects make use of trigonometry to determine how to create right angles in buildings. They do this by creating triangles with parallel hypotenuses (the part of the triangle that is perpendicular to its base) and using the sine function to calculate the height of the triangle.

Sines are used to determine the heights of vertical objects such as towers or walls. The sine of an angle is calculated by taking the ratio of the opposite over the adjacent side of the angle.

For instance, if the adjacent side is 4 and the opposite is 2, then the sine would be . This would equal 1/2 which is what we get when we divide 2 by 4.