We can use the sine function to determine the length of the rafters.
First, we need to find the height of the triangle formed by the rafter, the supporting wall, and the extension beyond the wall. We can use the sine function again to find this height:
sin(70) = height / 0.3
height = sin(70) x 0.3
height ≈ 0.275 m
Now, we can use the Pythagorean theorem to find the length of the rafter:
length^2 = width^2 + height^2
length^2 = 12^2 + 0.275^2
length ≈ 12.003 m
Therefore, the length of the rafters is approximately 12.003 m.
An architect designed a house that is 12.0 m wide. The rafters that hold up the roof are equal in length and meet at an angle of 70 degrees. The rafters extend 0.3 m beyond the supporting wall. How long are the rafters?
5 answers
Sorry. You need these steps.
If the height of the ridgeline is h meters above the eaves, then
h/6 = cos(70/2)°
h = 4.9
so the length of the rafters is
0.3+√(6^2 + 4.9^2) = 8.05 m
If the height of the ridgeline is h meters above the eaves, then
h/6 = cos(70/2)°
h = 4.9
so the length of the rafters is
0.3+√(6^2 + 4.9^2) = 8.05 m
Thank you for providing the additional steps! Here's the full solution with the given information:
Using the given angle of 70 degrees, we can split it in half to get two right angles of 35 degrees each. Then, we can use the cosine function to find the height of the ridgeline above the eaves (0.3 m beyond the supporting wall):
cos(35) = adjacent / hypotenuse
Since the adjacent side length is half of the width of the house (6.0 m), we can solve for the hypotenuse (which is the height we're looking for):
hypotenuse = adjacent / cos(35)
hypotenuse ≈ 7.317 m
However, this height is measured from the point where the rafters meet at the center of the ridgeline. If we want the height above the eaves (0.3 m beyond the supporting wall), we need to add the extra 0.3 m:
total height = 7.317 + 0.3
total height ≈ 7.617 m
Finally, we can use the Pythagorean theorem to find the length of the rafters:
length^2 = width^2 + height^2
length^2 = 12^2 + 7.617^2
length ≈ 14.618 m
However, we need to subtract the length of the overhang (0.3 m beyond the supporting wall) to get the actual length of the rafters:
actual length = length - overhang
actual length ≈ 14.618 - 0.3
actual length ≈ 14.318 m
Therefore, the length of the rafters is approximately 14.318 m.
Using the given angle of 70 degrees, we can split it in half to get two right angles of 35 degrees each. Then, we can use the cosine function to find the height of the ridgeline above the eaves (0.3 m beyond the supporting wall):
cos(35) = adjacent / hypotenuse
Since the adjacent side length is half of the width of the house (6.0 m), we can solve for the hypotenuse (which is the height we're looking for):
hypotenuse = adjacent / cos(35)
hypotenuse ≈ 7.317 m
However, this height is measured from the point where the rafters meet at the center of the ridgeline. If we want the height above the eaves (0.3 m beyond the supporting wall), we need to add the extra 0.3 m:
total height = 7.317 + 0.3
total height ≈ 7.617 m
Finally, we can use the Pythagorean theorem to find the length of the rafters:
length^2 = width^2 + height^2
length^2 = 12^2 + 7.617^2
length ≈ 14.618 m
However, we need to subtract the length of the overhang (0.3 m beyond the supporting wall) to get the actual length of the rafters:
actual length = length - overhang
actual length ≈ 14.618 - 0.3
actual length ≈ 14.318 m
Therefore, the length of the rafters is approximately 14.318 m.
oops - my mistake.
the length of the rafters is
0.3 + 6/sin35° = 10.76 m
the length of the rafters is
0.3 + 6/sin35° = 10.76 m
No problem! Let's use your new information to find the length of the rafters:
Using the 35 degree angle, we can use the sine function to find the height of the triangle formed by the rafter, the supporting wall, and the extension beyond the wall:
sin(35) = height / 6
height = sin(35) x 6
height ≈ 3.472 m
Now, we can use the Pythagorean theorem to find the length of the rafter, taking into account the overhang of 0.3 m beyond the supporting wall:
length^2 = 6^2 + (3.472 + 0.3)^2
length^2 = 36 + 14.92
length ≈ 4.279 + 0.3
length ≈ 4.579 m
However, we need to multiply this length by two since it's only one half of the rafter length:
actual length = 2 x length
actual length ≈ 2 x 4.579
actual length ≈ 9.158 m
Finally, we add the overhang to get the total length of the rafters:
total length = actual length + overhang
total length = 9.158 + 0.3
total length ≈ 9.458 m
Therefore, the length of the rafters is approximately 9.458 m.
Using the 35 degree angle, we can use the sine function to find the height of the triangle formed by the rafter, the supporting wall, and the extension beyond the wall:
sin(35) = height / 6
height = sin(35) x 6
height ≈ 3.472 m
Now, we can use the Pythagorean theorem to find the length of the rafter, taking into account the overhang of 0.3 m beyond the supporting wall:
length^2 = 6^2 + (3.472 + 0.3)^2
length^2 = 36 + 14.92
length ≈ 4.279 + 0.3
length ≈ 4.579 m
However, we need to multiply this length by two since it's only one half of the rafter length:
actual length = 2 x length
actual length ≈ 2 x 4.579
actual length ≈ 9.158 m
Finally, we add the overhang to get the total length of the rafters:
total length = actual length + overhang
total length = 9.158 + 0.3
total length ≈ 9.458 m
Therefore, the length of the rafters is approximately 9.458 m.