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

If you draw this you'll have a figure of a rectangle with a triangle on its top. The base of the triangle is 12 meters (equal to side length of rectangle). Half of the base is 6 m, and drawing a line as the height of the triangle, you can form two right triangles. Thus, the hypotenuse can be determined from

cos (angle) = adjacent / hypotenuse
cos (68) = 6 / hypotenuse
hypotenuse = 16.017

Since rafters extend 0.6 m, the total length of a rafter is
16.017 + 0.6 = 16.617 m

hope this helps? `u`

To find the length of the rafters, we can use the concept of right-angled triangles and trigonometry. Let's denote the length of the rafters as "x".

Given that the rafters extend 0.6m beyond the supporting wall, we can draw a right-angled triangle as follows:

/|
/ |
/ |
x / | 0.6m
/ |
/ |
/ |
/______|

We can see that the width of the house (12m) forms the base of the triangle. The length of the rafters (x) is the hypotenuse of the triangle. The angle between the base and the hypotenuse is 68 degrees.

Now, using trigonometry, we know that the cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is 0.6m and the hypotenuse is x. So, we can write:

cos(68 degrees) = 0.6 / x

To find the value of x, we can rearrange the equation:

x = 0.6 / cos(68 degrees)

Using a calculator, we can find the value of the cosine of 68 degrees and calculate x:

x ≈ 0.6 / cos(68 degrees)

x ≈ 0.6 / 0.3746

x ≈ 1.6 m

Therefore, the length of the rafters is approximately 1.6 meters.

To find the length of the rafters, we can use the trigonometric function cosine. The cosine function relates the adjacent and hypotenuse sides of a right triangle. In this case, the adjacent side is the overhang of the rafters, and the hypotenuse is the length of the rafters.

Let's break down the problem step by step:

1. Start by finding the length of the adjacent side of the right triangle formed by the overhang and the width of the house.
- The overhang is given as 0.6m.
- The width of the house is given as 12m.

Subtract the overhang from the width of the house to find the length of the adjacent side:

Adjacent side = Width of the house - Overhang
= 12m - 0.6m
= 11.4m

2. Now, we can use the cosine function to find the length of the rafters (the hypotenuse) using the angle of 68 degrees and the adjacent side we calculated in the previous step.
- Cosine(angle) = Adjacent side / Hypotenuse

Rearranging the formula to solve for the hypotenuse, we have:

Hypotenuse = Adjacent side / Cosine(angle)

Substitute the values we have:

Hypotenuse = 11.4m / Cosine(68 degrees)

3. Calculate the length of the rafters by evaluating the cosine of 68 degrees and dividing the adjacent side by it.
- Use a calculator or mathematical software to find the cosine of 68 degrees.
- Substitute the value of the cosine into the formula:

Hypotenuse = 11.4m / (cosine value)

Calculate the value using the numerical approximation of the cosine:

Hypotenuse ≈ 11.4m / 0.338

Hypotenuse ≈ 33.73m

Therefore, the length of the rafters is approximately 33.73 meters.