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· Old Methane Gas Cloud
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If someone could point me at someplace to learn the math for that that'd be awesome.
It's just high school trigonometry. (Actually I learned Tangent, Sine and Cosine in first year algebra.) With a book of trig functions and working everything into right triangles it's not difficult.

- The right angle 90° is not used in the calculations and the side opposite the right angle is called the Hypotenuse.

- By knowing the length of any two sides, the angles and third side can be calculated.

- By knowing one side and one angle the other angle and sides can be calculated.

Tangent of the angle = the opposite side divided by the adjacent side. Look up the Tangent and read the angle.

Sine of the angle = the opposite side divided by the hypotenuse. Look up the Sine and read the angle.

Cosine of the angle = the adjacent side divided by the hypotenuse. Look up the Cosine and read the angle.

The sum of the angles of a triangle always equals 180°. In a right triangle the two non right angles are complementary or subtract the angle that you know from 90° to determine the other angle.

When making a rectangular frame with mitered corners, the outside length of a side equals the inside length plus twice the width of the side.

It's the kind of thing that can be learned in a couple of hours if you accept the nomenclature and the process. I used to know where and how the trig functions were derived but it is not important.

A word of warning, some of the books of trig functions may indicate that the values of the functions are positive or negative. This has meaning for surveyors in coordinate geometry but for woodworkers always assume positive values.
 
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