An architect designs a house that is 12 m wide. The rafters holding up the roof are equal length and meet at an angle of 68°. The rafters extend 0.6 m beyond the supporting wall. How long are the rafters?

Hi - I was wondering if you could help me with this question. I'm not sure what they mean by rafters extending beyond the support wall and how I would be able to figure out the length if it extends.

base of right triangle = 12/2 = 6 m

angle at peak = 68/2 = 34 deg

we need the hypotenuse then add .6 m to each rafter
sin 34 = 6/L
L = 10.7
add .6
11.3 meters per rafter

Thank you for clarifying! Also appreciate how quickly you helped me. Very good math skills :)

Well, looks like those rafters are just trying to extend their reach and venture into the unknown beyond the wall! How adventurous!

Now, to answer your question, the length of the rafters can be determined using some trigonometry. The idea is to create a right-angled triangle, where the width of the house is the base and the rafter length is the hypotenuse. The angle formed by the rafters meeting is 68°.

To find the length of the rafters, you can use the tangent function, which is the ratio of the opposite side (the length of the rafters) to the adjacent side (the width of the house). So let's do some math magic:

tan(68°) = opposite/12

Now, we need to solve for the opposite side, which gives us:

opposite = tan(68°) * 12

But don't forget, the rafters extend 0.6 m beyond the supporting wall. So to find the total length of the rafters:

Total length of rafters = opposite + 0.6

Put it all together, and you have your answer! Happy rafter measuring!

Of course! I'd be happy to help you with that.

In architecture, rafters are the sloping beams used to support the roof of a building. When the question mentions that the rafters extend beyond the supporting wall, it means that part of the rafter goes beyond the edge of the wall.

To find the length of the rafters, we can use trigonometry. The given angle between the two rafters is 68°. Since the rafters meet to form a symmetrical triangle with a 68° angle at the apex, we can use the trigonometric functions to calculate the length of the rafter.

Here's how you can calculate the length of the rafter:
1. Draw a diagram to better visualize the problem.
2. Using the given information, label the known lengths and angles.
3. We'll be using the sine function because we know the angle and the opposite side length (0.6 m), which is the amount the rafters extend beyond the wall.
sin(68°) = 0.6 m / x
Here, x represents the length of the rafter.
4. Rearrange the equation to solve for x:
Multply both sides of the equation by x:
x * sin(68°) = 0.6 m
Divide both sides of the equation by sin(68°):
x = 0.6 m / sin(68°)
5. Use a calculator to evaluate sin(68°) and then solve for x:
x ≈ 0.6 m / 0.92718 (using a calculator)
x ≈ 0.647 m

Therefore, the length of the rafter is approximately 0.647 meters.

Certainly! I'd be happy to help explain how to solve this problem.

In this question, the rafters refer to the sloping beams that support the roof of the house. The architect has designed the house with rafters that extend beyond the supporting wall by 0.6 m.

To find the length of the rafters, we can use the concept of trigonometry, specifically the sine function. The formula for finding the length of one of the rafters can be expressed as:

Rafter Length = (House Width / 2) / sin(Angle)

Let's break down the steps to solve the problem:

1. Convert the angle given in degrees (68°) into radians by using the formula:
Angle in Radians = Angle in Degrees * π / 180°

For this problem, the angle in radians would be:
Angle in Radians = 68° * π / 180°

2. Calculate the sine of the angle obtained in radians. You can use a calculator or a math library function. Let's denote this value as "sinAngle".

3. Substitute the given values into the formula to find the length of the rafters:
Rafter Length = (12 m / 2) / sinAngle

4. Calculate the value of "Rafter Length" using the formula and the calculated value of "sinAngle".

5. Finally, add 0.6 m to the calculated rafter length to account for the extension beyond the supporting wall.

By following these steps, you can determine the length of the rafters in this scenario.