A-frame for Swing
Date: 07/26/97 at 12:07:31 From: Dennis Ribblett Subject: A-frame for swing out of 4 by 4's I am trying to build a stand for a swing. The ends are A-frames out of 4 by 4's. The brace for the top is a 4 by 4. The legs are to be 4 feet apart and the length of each 8 feet. I need to miter the bottom of each of the 8 foot sections and the top of each to join to the 4 by 4 brace. What is the angle of the miter cut?
Date: 07/29/97 at 10:06:15 From: Doctor Rob Subject: Re: A-frame for swing out of 4 by 4's Let's see. Let this be an approximate picture: __ Q | | /|__|\ / /\ \ / / \ \ / / \ \ / / \ \ / / \ \ / / \ \ 8 feet / / \ \ / / \ \ / / \ \ / / \ \ / / \ \ / / \ \ / / \ \ ---- R ---- P <--------- 4 feet -------> I put the angle at point P equal to A. Then from looking at similar triangles (the big one a right triangle with hypotenuse PQ = 96, the small one a right triangle with horizontal hypotenuse PR), I get the equation 4 ----- + 22 sin A ---------- = cos A. 96 A numerical solution produces the answer A = 74.18859 degrees, or, for your purposes, 74 degrees. It turns out that PR = 4.15730 inches, or nearly 4+5/32 inches. Of course, this is assuming that your 4-by-4s are really 4.00000 inches square, which is very likely to be false. Nevertheless, this answer will be very close to correct. By the way, I think I would put the feet farther apart for safety. If they are 8 feet apart, and therefore the end triangles are equilateral, the mitre angle would be 60 degrees. Of course this depends on how firmly the feet are anchored. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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