How to Use Trigonometry in Carpentry

By Ezmeralda Lee

Trigonometry is something that most people say they can't do. The funny part is that 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. 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 the Angle = opposite hypotenuse cosine of the Angle = adjacent hypotenuse tangent of the Angle = opposite Adjacent

When trying to determine the length of the opposite you would use the following equation:
tan 55 Deg = opposite 100” 100” x tan 55 Deg = opposite 100’ x 1.42 = opposite opposite = 142”

When trying to determine the length of the hypotenuse you would use the Pythagorean theorem: a2 + b2 = c2 1002 + 1422 = c2 c2 = 30164 c = 173.68”

If you need to know the measurement of the final angle, you must first know that the angles add up to 180 Degrees.
90 Deg + 55 Deg = 180 Deg – unknown 145 Deg = 180 Deg – unknown unknown = 35 Deg

Tip

When making calculations for a job, use a calculator if one is available. Wrong calculations can cost a job a lot of money and wasted time. Trigonometry is used in many other carpentry applications, including site layout tasks that require making angular measurements. These tasks might include laying out building foundation lines and determining elevations by trigonometric leveling.
Roof slopes and stair measurements are nothing more than right angle problems.
Purchasing a good tangent wheel can help speed up the process of figuring angles. Carry a notebook. Every time you need to work out angles or lines, document it, you may be able to use it again and save yourself some time. When laying out a foundation, diagonal measurements are a must have. The diagonal on a square foundation helps to ensure that your foundation is indeed square.
Other jobs that may use trigonometry are navigation, land surveying, mathematics, science, engineering, architecture, cartography, computer graphics, machining, meteorology, music theory, oceanography, phonetics, seismology, and statistics.

Warning

Using trial and error to figure curves and angles can be very costly and time consuming. Trigonometry functions will help to greatly reduce this. The trigonometry functions listed above only apply to right angle applications. The trigonometry equations are the same in triangles that do not have right triangles if you divide it in half and create two equal right triangles. After figuring one half of the new pair of right triangles, be sure that you accurately figure the angles and sides when looking at the triangle as a whole.