A trigonometry question for mathmeticians

[gnvqsos]

Are you sure of these dimensions? 21.5 degrees is a very shallow pitch. What sort of roof covering does it have?

 

This is a standard gradient for a domestic roof on many Edwardian terraces,and any steeper angles will unduly stress the copper nails/hooks used to secure slates.

[Jake Elwood]

Here's a question. By "horizontal line" does he mean from the edge to the top, or the entire length of the roof from one edge to the other?

 

If the latter, my calculation will be wrong. I know less than nothing about roofing; my only contribution is to plug the numbers in and report the result.

 

I was expecting something about 20 degrees. It is a shallow pitch extension roof and I got some man made slates which the manufacturers said could go down to 17.5 degrees. The sodding window cleaner has cracked a few of them so I am looking at replacing the slates. There are not that many on the market that can go down to this shallow pitch so I need an accurate degree before I start looking.

 

The horizontal is from the bottom slate to in line with the lead upstand or top slate. The vertical is the height from the bottom slate to the top slate. I cant measure the slope because I cant reach it.

 

In other words look at a triangle with the second longest side on the base and the shortest side upright. It is of course not the 90 degree angle but the acute angle degree I am looking for.

[Jake Elwood]

Just found this but to tired to try and understand it.

 

http://www.mathsisfun.com/algebra/trig-finding-angle-right-triangle.html

[quisquose]

So I've got this triangle. Sides are 5cm x 7cm x 10cm. What are the internal angles?

 

( Just want to check what I told my daughter for her homework )

 

 

Edit: Which was cosA = (b2 + c2 - a2) / 2bc

[handypandy]

No need for such long measurements. The simplest way of obtaining your pitch is with this guide clicky

[HeadingNorth]

I was expecting something about 20 degrees. It is a shallow pitch extension roof and I got some man made slates which the manufacturers said could go down to 17.5 degrees. The sodding window cleaner has cracked a few of them so I am looking at replacing the slates. There are not that many on the market that can go down to this shallow pitch so I need an accurate degree before I start looking.

 

The horizontal is from the bottom slate to in line with the lead upstand or top slate. The vertical is the height from the bottom slate to the top slate. I cant measure the slope because I cant reach it.

 

In other words look at a triangle with the second longest side on the base and the shortest side upright. It is of course not the 90 degree angle but the acute angle degree I am looking for.

 

Given that information - and assuming your measurements to be correct - 21.5 degrees is the correct answer.

 

(The tangent of the angle you're after is equal to the vertical distance divided by the horizontal, so we know that the tangent of the angle is 1170/2970, which is 13/33 or 0.393939.... and the inverse tangent of that, the angle whose tangent is that value, is 21.5 degrees.)

[Jake Elwood]

Thanks HN, I remember it being around that figure when I had the extension done. I had to prove it to the building society's surveyor and then prove the slates fitted was suitable at that pitch.

 

Got to go slate and tile hunting now.