Good afternoon, dear guests and subscribers of my channel!
The topic of today's article, in my opinion, is interesting. It connects mathematics with real objects, or rather, with the roofs of our houses. And these are not just abstract triangles with which we are used to solving problems from textbooks, these are living structures that protect the living space from bad weather.
Dima, he is also a professional foreman who has devoted almost 40 years to roofing systems. He has two brigades, not just brigades, but a real team of 5 professional craftsmen.
We do not meet often, twice a year, but as we see each other, I see so many permanent five people who have been entrenched for 6-7 years and work harmoniously together.
It all started with a call to Dima's phone, at that moment he opened his journal and made a record of another object. I spied, everything is planned for 10-12 objects ahead. I ask, how, they say, you are busy with work every day, and others suck your thumb, what does it depend on? Of course, from my side it was a stupid question, but I got the answer.
Of course, everything depends on professionalism, and a professional is speed + quality. Then Dmitry shared how he was looking for handy guys. After all, working only with your hands is one thing, He speaks, and this is a roofer, and if the head is included in the process of work, then this professional roofer.
In fact, working with roofs or constructing a frame is all the work of a carpenter and pure water - mathematics, geometry, trigonometry and stereometry. Dmitry has three questions for the candidates, but one of them I liked the most. This is a kind of geometric problem that shows the possession of the material part.
Dima voices it like this: How to calculate the angle of a hip (corner) rafter or valley, if you know the angle of the roof? Hold a sheet and a pencil to help, let me think 15 minutes.
In other words, a person is invited without going up to the roof - to calculate the angle of the hip cut rafter leg (angle β) relative to the horizon, knowing only the angle of inclination of the main rafter legs (angle α).
Class!
Of course, not everyone can give an answer right away, but the foreman sees attempts to calculate the angle, and if the head works in the right direction, then the master replenishes the ranks of this team.
In fact, the formula is derived in 4 steps. I would not like to overload the article with evidence, but below - in the first comment I will describe everything.
The formula is:
tg (β) = tan (α) / √2
or
β = arctan (tan (α) / √2)
Basically, all roofers know that this angle is different from the angle of the main rafters that form the roof slope. But how to calculate - not everyone knows.
Using a calculator in any phone, this angle can be calculated in 3 minutes knowing the formula and for this there is absolutely no need to climb onto the roof and draw vertical lines on the rafters with a pencil and a plumb line legs.
This is one of many examples where mathematics can save you more than one hour.
Thank you for your attention, good luck with your construction.
P.S.
The same principle of the tangent of angles is laid down in Swenson's square or roofer's square. This square - "magic wand" for carpenters:
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