How To Build A Sawhorse 7

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Build A Sawhorse At An Exact Height By Calculating Sawhorse Leg Length With Angle Cosines

When the top piece of a sawhorse is to be built to a specific height above the ground, the sawhorse leg length can be calculated from the formula: H2 = X1/Cosine A1 * Cosine A2. See figure 7 for definitions and calculations of H2, X1, A1 and A2. The cosine of an angle in a right triangle is the resulting ratio when the angle's adjacent side is divided by the hypotenuse. A right triangle has a 90 degree angle in it. A sawhorse leg projects from the top piece at the two angles, A1 and A2, and forms two different right triangles with these angles. To visualize the two triangles, think of the sawhorse leg moving first from X1 to H1 to form the triangle with angle A1, then moving next from H1 to H2 to form the second triangle with angle A2. Note that the A2 right triangle sides, H1 and H2, figure 7 bottom, appear vertical but are actually tilted towards you at the angle of H1, figure 7 top. The two triangles' cosines of angles A1 and A2, hypotenuse H1, adjacent side X1, and adjacent side H1 are used to calculate the leg length H2. Note that the hypotenuse H1 in the triangle with angle A1 becomes the adjacent side H1 in the triangle with angle A2. The following formula (in sentence form) is used to calculate the sawhorse leg length. The Leg Length H2 equals the Height of the Sawhorse X1 divided by the Cosine of Angle A1 and the Cosine of Angle A2. H2 = X1/Cosine A1 * Cosine A2. Note that cosines A1 and A2 should be multiplied together first before being divided into the height X1.  (/ means divided by  and * means multiply). The formula: H2 = X1/Cosine A1 * Cosine A2 is derived from the following formulas: H2 = H1/Cosine A2. H1 = X1/Cosine A1. H2 = X1/Cosine A1/Cosine A2. H2 = X1/Cosine A1 * Cosine A2

Example of How to Use the Formula: H2 = X1/Cosine A1 * Cosine A2
X1 = 24 inches = Height of the Sawhorse Top Piece
A1 = 15 degrees, Cosine A1 = 0.966
A2 = 20 degrees, Cosine A2 = 0.940
Cosine A1 * Cosine A2 = (0.966)(0.940) =  0.90804
H2 = X1/Cosine A1 * Cosine A2
H2 = 24 inches/(0.966)(0.940) = 24 inches/0.90804 = 26.431 inches = 26.4 inches = Sawhorse Leg Length

Figure 7 Calculate The Leg Length Of A Sawhorse By Using Angle Cosines

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1.Sawhorse: Sawhorse Side View Components & Dimensions.
2.Sawhorse: Sawhorse Front View Components & Dimensions.
3.Sawhorse: Sawhorse Leg Measurements.
4.Sawhorse: Sawhorse Top Piece Lay Out.
5.Sawhorse: Saw Cut Angle Lines On Sawhorse Top.
6.Sawhorse: Sawhorse Plywood End Piece.
7.Sawhorse: Calculate Sawhorse Leg Length & Exact Height With Angle Cosines.

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Ronald Hunter

All images and text are copyright Ronald Hunter 2005 to 2011