SOLUTION: I'm a toymaker. I'm building a toy castle.The watchtower is an octagon. The roof of the tower is made of 8 triangular pieces. The slope of the roof should be 45°. I'm trying to cal

Algebra ->  Triangles -> SOLUTION: I'm a toymaker. I'm building a toy castle.The watchtower is an octagon. The roof of the tower is made of 8 triangular pieces. The slope of the roof should be 45°. I'm trying to cal      Log On


   

Question 579455: I'm a toymaker. I'm building a toy castle.The watchtower is an octagon. The roof of the tower is made of 8 triangular pieces. The slope of the roof should be 45°. I'm trying to calculate the corners on wich to cut each part of the roof so they fit perfectly. I came up with the following formula but have no way to check it:(((180-(360/Z))/90)*H)/2
In this formula Z refers to the number of sides and H to the slope of the roof, calculated from a vertical view. English is not my native language, so I hope you can understand wat I want.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The way I read your formula, for H=45 and Z=8, we would get

but I got a different result.
This is the way I calculate it for a 45 degree slope.
View from the top
and
View from the side roof piece
The measure of the angles at the bottom of the roof pieces should be 73.7%5Eo because
tan%2873.7%5Eo%29=2%2Bsqrt%282%29 .
The other angle would measure 32.6%5Eo .
However, maybe it is easier to make the height of the triangle %282%2Bsqrt%282%29%29%2F2 times (about 1.707 times) the length of the base.