Calculating Length of Cottage Rafters

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In summary, Kelly designed a cottage with a 15 m wide roof supported by identical rafters meeting at a 80 degree angle. The rafters hang over the supporting wall by 0.5 m. To find the length of the rafters, trigonometry can be used by setting up an isosceles triangle with base 15m and top angle 40 degrees. The length of the opposite side can be found using sine, and the rafters will be the hypotenuse of the right triangle. However, it is unclear from the question whether the 0.5 m overhang is added to the base or the rafters themselves.
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aisha
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Kelly designs a cottage that is 15 m wide. The roof rafters are the same length and meet at angle of 80 degrees. The rafters hang over the supporting wall by 0.5 m. How long are the rafters?

Im not sure how to set up this question will it involve algebra?

I don't know how the cosine law or sine law can be used can someone help me out please? :smile:
 
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It requires, of course, trigonometry. You don't need the sine and cosine laws since this can be done entirely with right triangles.

First draw a picture! You have an isosceles triangle with the roof forming the two top (equal) lines. Since "the rafters hang over the supporting wall by 0.5 m" (I am assuming that that is measured horizontally) the length of the base of that triangle is 15 m (the 15 m width plus the two 0.5 m overhang). You can get right triangles by drawing the vertical line down from the crest of the roof (i.e. the top angle). That way you have two identical right triangles. The angle at the top is (1/2)(80)= 40 degrees and the length of the "opposite side" is (1/2)(16)= 8 m. You know that
sin(angle)= opposite/hypotenuse so sin(40)= 8/x. Of course, the rafters ARE the hypotenuses.
 
  • #3
I think my diagram doesn't look right because I don't understand why you added the 0.5 to the base. why wasn't it added to the rafters?

Can someone please explain? :confused:
 
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  • #4
aisha said:
Kelly designs a cottage that is 15 m wide. The roof rafters are the same length and meet at angle of 80 degrees. The rafters hang over the supporting wall by 0.5 m. How long are the rafters?

Im not sure how to set up this question will it involve algebra?

I don't know how the cosine law or sine law can be used can someone help me out please? :smile:
What I do not get is how are the rafters arranged. Is there a diagram with it or are you simply given the question as it is written?? Also, why does the question say that the rafters are the same length and then say they are 0.5m longer??

Answer these and the answer might be obvious.

The Bob (2004 ©)
 
  • #5
aisha said:
I think my diagram doesn't look right because I don't understand why you added the 0.5 to the base. why wasn't it added to the rafters?

Can someone please explain? :confused:

That possibility had occurred to me- you might want to ask your teacher to clarify it. I decided that the words "hang over" referred to the distance out from the wall.

If you think it means that the length of the rafter, past the wall, is 0.5 m, do the problem with base 15 m so the "opposite side" of the right triangle is 7.5 m (the fact that the other way gives an integer length here may have influenced me!). Now solve for the hypotenuse of that right triangle and then add 0.5 m to it.
 
  • #6
ok thanks soo much, I will ask her for sure! :smile:

Bob there was no diagram just the question I didnt write it so I don't know why it says what it does. :smile:
 
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1. How do I calculate the length of cottage rafters?

To calculate the length of cottage rafters, you will need to use the Pythagorean theorem. First, measure the horizontal distance from the center of the ridge beam (top of the roof) to the outside of the wall. Next, measure the vertical distance from the center of the ridge beam to the top of the wall plate. Finally, use the formula c² = a² + b² to calculate the rafter length, where c is the rafter length, a is the horizontal distance, and b is the vertical distance.

2. What other information do I need to know in order to calculate the length of cottage rafters?

In addition to the horizontal and vertical distances, you will also need to know the pitch of the roof. The pitch is the slope of the roof, and it is typically expressed as a ratio of rise over run. For example, a roof with a 6/12 pitch means that for every 12 inches of horizontal run, the roof rises 6 inches.

3. Can I use a rafter calculator to determine the length of cottage rafters?

Yes, there are many online rafter calculators available that can help you determine the length of cottage rafters. However, it is important to double-check the results and make sure they align with the Pythagorean theorem formula before using them for construction purposes.

4. Is there a specific formula for calculating the length of cottage rafters for different roof shapes?

The Pythagorean theorem can be used to calculate the length of cottage rafters for any roof shape, as long as the horizontal and vertical distances are measured correctly. However, the pitch of the roof will affect the length of the rafters, so it is important to use the correct pitch in the formula.

5. Are there any other factors that may affect the length of cottage rafters?

In addition to the pitch of the roof, the type and size of the building materials used for the rafters may also affect the length. It is important to consult with a structural engineer or follow building codes to ensure that the rafters are strong enough to support the roof.

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