UnitMath ( Angle Notes )
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The following figure shows a board with the angle we want to cut
The next figures show how the gauge would have to be set to make this cut. Note the setup on the right is not recommended.
The next figure shows what most saw gauges measure ( the angle to the normal ).
Gauge angle = 90 deg - Desired angle
Desired angle = 90 deg - Gauge angle
With this in mind you may want to add another angle in the output like:
HipAngleGauge: 90 deg - HipAngle.
sin( angle ) = width / hypotenuse
cos( angle ) = x / hypotenuse
tan( angle ) = width / x
So given the width of the board and the length of the hypotenuse we can find the cut angle. You will notice that the angle below is not exact, that is because our lengths are not exact. Longer distances will give more precise results.
width: 4 inch + 1/2 in pm 1/32 inch;
hypotenuse: 7 inch + 3/8 inch pm 1/32 inch;
angle: asin( width / hypotenuse ) as deg; ~ ( 37.1 to 38.1 ) deg
If the piece we are cutting is very wide it much easier to draw a cut line and use a portable saw. For this we would calculate x. The following calculation is for a 4 foot wide piece of plywood with a 30 degree angle.
x: 4 ft / tan ( 30 deg ) as inch & in/16 ~ ( 83 inch + 2.2 in/16 )
If you hold to those tolerances you can get very accurate angles. For example the above cut is precise to better than a tenth of a degree.
atan((4 ft pm 1/32 inch) / ( 83 inch + 2.2 in/16 pm 1/32 inch )) as deg ~ 30.0 deg