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Episode 43 – Angles – A simple problem and a not so simple one

In this episode I discuss the simple problem of making boards or pipes butt up to each other correctly for angles other than 90 degrees. Later I discuss the complete calculations for the real-life problem of my grape arbors discussed in the last episode. That is not a simple set of calculations.

The key to get boards or pipes to butt up to each other is bisect the angle they are forming. This simply means divide the cut in half so both boards will be the same length at the cut.
In this picture I show two possibilities to cut two  boards to fit together and form a 120 degree angle.  The 120 degree angle would be used if we were making a hexagon shaped box or room, for example a gazebo.  In the top example, the cut of the boards is not divided evenly, and the results is not good.   In the bottom example both boards are cut to form a 60 deg. cut and both boards butt up to each other with good results.

The following shows the steps necessary to correctly build corner post for the grape arbor I talked about in Episode 42 – An Angle Mistake.   In the first step. I assume that the pole coming off the post is at a 30 degree angle from horizontal and is 48″ long.  The problem is to determine how much it projects from the fence and how high the end of the pole is above the top of the post.The next step is to determine the horizontal radius of the corner post.   This post will be at a 45 deg angle to both the posts along the back fence and the ones along the side fence.  The view in this picture is above looking downward.
The final step is to look at the size of the corner post and determine the length of the pole and the angle of the pole rise to obtain the the horizontal distance of 58.79″ calculated in the previous step and the vertical rise of 24″. calculated in the first step.

This looks long and complicated, and it is.  However, it is a real problem in a real situation, so there really is no easy way out.   Good luck on following the reasoning.  Rolling up your sleeves and doing the work of understanding it will pay off eventually, because sooner or later you will have a similar problem if you design and build things.





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