How Is Trigonometry Used In Architecture?

 

I find it interesting that people can take a drawing and translate it into a real building that can either look normal or like something that came to us from the future. The people who create these visions and translate them from their heads to paper for the builders to turn it into reality. Did you know that architects use trigonometry in their work?

Trigonometry helps architects calculate the slope or pitch of the roof, ground surfaces, light angles, structural loads, and the heights and width of structures.  All of these things are used to create a mathematical representation that a contractor can follow when constructing the building.

Often time the slope of the roof is given in degrees and must be changed into actual measurements. This requires people to set the tangent x = to rise(y)/run(x) to change from degrees to actual lengths for the difference of y and the difference of x. Usually, the architect has the degrees and one of the values of x or y.  For instance you might what to know for a tangent of 38 degrees what the rise or y value is if the run or x value is 12 feet.  so Tan 38 degrees = y/12 and solve to find out the value of y. Ground surface is defined as the intended or finished grade of the surface of the ground at the site of the well or ground.  The grade is found using trig much in the same way as done for the slope of the roof.

As far as light angle goes, the trig is used to figure out how much area one light will illuminate.  For instance, if the architect is looking at using LED lighting, they have to determine if the lights are omnidirectional and will light everything evenly in a circle or if the lights are directional and light only in one direction.  The beam angle refers to the angle in which the luminous flux leaves the light fixture and depending on how far the light travels, it will create a cone of the corresponding diameter. Usually beam angles are listed in degrees and range from 10 to 120 degrees depending.

The beam angle only looks at where the light is at least 50 percent intensity.  Field angle refers to the part of the light ranging from 1 to 49 percent intensity, so the beam angle is inside the field angle and the only place the light is a full 100 percent is in the center of the cone of light.  It is recommended that architects use 120 degrees to provide basic lighting in a room and 90 degrees for corridors and hallways. 

As mentioned before, architects can use to calculate the structural loads of the building and other things.  Architects need to understand how all the forces work on a building using vectors which have magnitude and directions.  By applying trigonometry to the vectors, they can determine loads and forces. In addition, trig is used to figure out the load that the tresses are being exposed to.

So there are lots of ways trig is used by architects when they design buildings.  Let me know what you think, I'd love to hear.  Have a great day.