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# How to Calculate Trig in Building a Roof

Updated February 20, 2018

Trigonometry is a branch of mathematics used to calculate angles and leg lengths of right triangles. Trigonometry has several applications in the real world, such as determining the height and slope of a pitched roof. Trigonometric calculations using the Pythagorean Theorem can also be used to determine how much material -- such as the minimum necessary length of a support beam -- will be required to construct a roof.

Determine how high from the top of the support walls that the roof will be, and write this proposed measurement down as the "rise" measurement of the roof. Measure the width of the building from one end of one of the support walls to the other end. Record this measurement.

Divide the building width measurement by two, and write this measurement down as the "run" measurement of the roof.

Calculate the square of the rise measurement and add it to the square of the run measurement. For example, if the rise measurement is three feet and the run measurement is 12 feet, add three squared (9) plus 12 squared (144) to get 153. Take the square root of this number to get the minimum required length of the roof slope beams to be used. For this example, each roof slope beam must be at least 12.37 feet long.

#### Things You'll Need

• Measuring tape
• Pen or pencil
• Paper
• Scientific calculator