Good afternoon, dear guests and subscribers of my channel!
Recently, a familiar professional carpenter showed the masterful use of a square as a protractor. Now I know that not only corners can be built with an ordinary square. 45° and 90°, and even 10 °, 20 °, 30 °, 40 °, 50 °, 60 °, 70 ° and 80 °.
I confess that before writing the article, I spent a lot of time searching for this topic on the Internet - no one offers this method, so this article is the primary source ...
The method is called: The Rule of Eleven.
Why exactly "eleven"? When constructing any of the corners, we always need to set aside 11 centimeters first. According to this technology, the angle will be built along a right-angled triangle, or rather, along its two legs, one of which is 11 cm.
The very first thing, with the help of a square, draw a perpendicular 11 cm away from the edge of the workpiece. In the photo - the perpendicular is highlighted in red:
We now have a marked segment of 11 cm. and perpendicular. If any point of this perpendicular is connected to the corner of the workpiece, then we get a right-angled triangle. And then, a little theory :-)))
From the school geometry course, we know that it is the ratio of two legs of a right triangle that determines trigonometric functions of angle (tangent and cotangent)
Building 20° and 70°
Look! Putting aside 11 cm. horizontally and 4 cm. vertically we get an acute angle of 20°:
In the photo, on the constructed perpendicular, I mark 4 cm. and connect the ends of the segments:
I prove: Below, under each illustration, to check the value of the angle, I specifically calculate the inverse trigonometric function - the arctangent (arctan) as proof.
The arc tangent of the ratio of legs 4 and 11 gives us the angle 19,98°. An error of two hundredths is definitely negligible. Accordingly, the adjacent angle will be 70.02 ° or ~ 70 °.
Construction 40 ° and 50 °
Next angles 40° and 50° obtained from two legs: 11 cm. horizontally and 13 cm. vertically. I prove:
Construction: On the same perpendicular we put a mark of 13 cm. and connect the ends. We get the angle in 49,76°. - the error is scanty and is no more than the tip of the nail, so this can be considered an angle in ~50°.
Build 30 ° and 60 °
By putting aside 19 cm. vertically, we get an angle of 60°.
Surprisingly, it is the 11 cm leg. gives us the integer value of the second leg, which is the basis of this rule.
Without a goniometer at hand, we can easily build the angles we need!
Now all that remains is to stick a tag on the square, so as not to forget about it at first :-)))
P.S.
Of course... I forgot about 10 °, but this angle is very rarely used by carpenters. It is enough to set aside 2 cm on the perpendicular. when the length of the second leg is 11 cm, then the angle will be ~ 10 °, and the adjacent one will be 80 °.
Let's summarize:
Without a protractor / protractor at hand, we just need to remember 5 numbers: 2,4,13,19 and basic 11, to plot any of the corners in 10 ° increments. In this case, we only need a ruler!
Good luck to you!
MY INTERESTING ARTICLES:
“Just one simple task baffles almost all roofers,” said the foreman. Roof geometry
Orientation: 3 cool ways to find out the height of an object without climbing on it (photo examples)
Finished the stairs. Valuable personal experience: how to save up to 50% on everything? (welded frame, steps, fencing)