How to Find Angles With a Framing Square And a Tangent Table

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A framing square consists of a long arm and short arm that meet at a right angle. The long arm is the body and the short arm is the tongue of the framing square. A tangent table is a list of angular measurements and the corresponding tangent values. Carpenters use a framing square and tangent table to find an included angle in a right triangle, such as those on a blue print.

Things You'll Need

  • Calculator
  • Position the framing square so that the legs of the framing square align with the legs of the right triangle.

  • Measure the legs of the right triangle with the measurement markings on the framing square. Assume for this example that the leg opposite the angle you wish to calculate is 2 inches in length. Assume the leg adjacent to the angle you wish to calculate is 3 inches in length.

  • Divide the length of the opposite leg of the right triangle by the length of the adjacent leg of the right triangle to obtain the tangent of the angle you wish to measure. The length of the opposite leg is 2 inches and the length of the adjacent leg is 3 inches in this example. The tangent of the angle you wish to measure is therefore 2 divided by 3 and equals 0.667.

  • Locate the tangent value on a tangent table that is closest to the tangent value you obtained in step 3. Science Projects provides a table of tangent values for each whole degree angle below 90 degrees. The reference tangent value that is closest to the example tangent value of 0.667 is 0.6744.

  • Locate the angle measurement on the tangent table that corresponds to the reference tangent value from step 4. The reference tangent value in this example is 0.6744, which corresponds to 34 degrees. The angle in this example therefore measures approximately 34 degrees.

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