Let us calculate the length of the roof rafter as shown in the below drawing.
👀 What are the different terms used in roof slope calculations?
So that you will understand the calculation steps clearly.
The length of the roof rafters is calculated in three different methods based on the available data. Let us go through, all of them as explained below.
1. Roof rafter with pitch:
Given data:
Span = 20 ft.
Pitch = 7 /12
As you know,
Run = [span ÷ 2]
= [ 20 ft. ÷ 2]
= 10 ft.
Here,
Pitch = [rise/run.]
i.e. ( 7 / 12 ) = [ rise / 10 ft.]
By cross multiplication,
Rise = [ (7/12 ) × 10 ft.]
= 5.833 ft.
By Pythagoras' theorem,
AB2= AC2 + BC2
i.e. rafter2= rise2 + run2
Rafter = √ rise2 + run2
Rafter = √ (5.833)2 + (10)2
= √ 34.027 + 100
= √ 134.027
= 11.577 ft.
Length of the roof rafter = 11.577 ft.
2. Roof rafter with an angle & span:
Span = 20 ft.
Angle θ = 25°
As you know,
Run = [span ÷ 2]
= [ 20 ft. ÷ 2]
= 10 ft.
By trigonometry,
sinθ = opposite / hypotenuse
In the above triangle,
Side AB = rafter = hypotenuse
Side BC = run = opposite.
So,
Sin25° = [ 10 ft. ÷ hypotenuse]
0.4226 = [ 10 ft. ÷ hypotenuse]
By cross-multiplying,
Hypotenuse = [10 ft. ÷ 0.4226 ]
= 23.663 ft.
The length of the roof rafter = 23.663 ft.
3. Roof rafter with an angle & rise:
Given data :
Rise = 8 ft.
Angle θ = 25°
By trigonometry,
cosθ = adjacent / hypotenuse
In the above triangle,
Side AB = rafter = hypotenuse
Side AC = rise = adjacent.
So,
Cos25° = [ 8 ft. ÷ hypotenuse]
0.906 = [ 8 ft. ÷ hypotenuse]
By cross-multiplying,
Hypotenuse = [8 ft. ÷ 0.906 ]
= 8.83 ft.
The length of the roof rafter = 8.83 ft.
hell ca you explain to me how is that your able to get 0.906 from Cos25*=[8ft/hypotenuse, i dont how you got that answer. thank you for your time.
ReplyDeleteBy trigonometry, value of cos25° is 0.906. You can use your calculator to find the value.
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