Trigonometry, once you understand the basics, is fairly easy to use. The sine curve/cosine curve model works great for electrical engineering, but isn’t very useful for building math. Really, just the ++ quadrant of a unit circle is sufficient for every trigonometry problem you’re likely to encounter as a carpenter.
This is the intersection of an 8/12 roof and a 5/12 roof. The cricket has an 8/12 slope on one side, and a 5/12 on the other. Two of the valleys are regular, they are at an angle of 45º to plan. The other two valleys are irregular, one side is 5/12, the other 8/12, and the valleys lie at an angle other than 45º to plan. This requires a slightly more sophisticated approach than the conventional solutions.
Here’s a simple isometric of the basic idea, with the individual triangles lined out in colors. The trick is to determine a common…
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