To Build A Sawhorse 7
the top piece of a
sawhorse is to be built to a specific height above the ground,
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
with angle A1, then moving next
from H1 to H2 to form the second triangle with angle A2. Note
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,
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
together first before being divided into the height X1. (/
divided by and * means multiply). The formula: H2 = X1/Cosine
* 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
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 = 24 inches/(0.966)(0.940) = 24 inches/0.90804 = 26.431 inches =
26.4 inches = Sawhorse Leg Length
Calculate The Leg Length Of A Sawhorse By Using Angle Cosines
Side View Components & Dimensions.
Front View Components & Dimensions.
Top Piece Lay Out.
Angle Lines On Sawhorse Top.
Plywood End Piece.
7.Sawhorse: Calculate Sawhorse Leg Length & Exact
Height With Angle Cosines.
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images and text are copyright Ronald Hunter 2005 to 2011