How to Use Trigonometry in Carpentry

By Ezmeralda Lee

Trigonometry is something that most people say they could never do. The funny part is, it is really easy. Carpentry calls for trigonometry more than you might think. Every time a carpenter makes an angled cut, the measurement of the angle or the adjoining lines must be figured out. Trigonometry is used in many other carpentry applications, including site layout tasks that require using angular measurements. These tasks might include laying out building foundation lines and determining elevations by completing trigonometric leveling. You could do this the slow (and potentially wrong) way, or you could use trigonometry. Here is the easy "trigonometry" way to figure it out.

Learn the trigonometric function for a right triangle:Sine of angle = Opposite/hypotenuseCosine of angle = Adjacent/hypotenuseTangent of angle = Opposite/adjacent

Assume you are cutting a support board for a table mounted against a wall, and you want the support to sit at a 35-degree angle. You need to find the resulting height of the bench if the bench is 48 inches wide. To determine the height of the bench, use the following equation: Tan 35 degrees = Opposite/48 inches48 inches x tan 35 degrees = Opposite48 inches x 0.70 = OppositeOpposite = 33.5 inches

Determine the length of the hypotenuse, or support. Use the Pythagorean theorem: a^2 + b^2 = c^248^2 + 33.5^2 = c^2c^2 = 3426.25c = 58.5 inches

Determine the measurement of the final angle. You must first know that the angles add up to 180 degrees: 90 degrees + 35 degrees = 180 degrees - unknown125 degrees = 180 degrees - unknownUnknown = 55 degrees

Document your measurements. Keep a notebook with a record of all of your measurements. This will speed up the process the next time you need to make the same measurement. You will able to refer back to it instead of spending time on new calculations.