An A-frame house is 40 feet high and 30 feet wide. Find the angle that the roof makes with the floor. Round the angle nearest degree.
Assuming that the peak of the house is in the centre of the width.
tanØ = 40/15 = 8/3
Ø = appr 69°
To find the angle that the roof makes with the floor of an A-frame house, you can use basic trigonometry.
1. Identify the triangle formed by the height (opposite side), half the width (adjacent side), and the hypotenuse of the triangle.
2. In this case, the height of the house, which is 40 feet, represents the opposite side of the triangle, and half the width, which is 30 feet/2 = 15 feet, represents the adjacent side.
3. Use the tangent function, which is defined as the opposite side divided by the adjacent side, to find the angle. The tangent of an angle is equal to the opposite divided by the adjacent side.
tangent(angle) = opposite/adjacent
4. In this case, the equation becomes:
tangent(angle) = 40/15
5. Calculate the tangent of the angle.
tangent(angle) ≈ 2.6667
6. Use the inverse tangent function (arctan) to find the measure of the angle.
angle ≈ arctan(2.6667)
7. Calculate the arctan of 2.6667.
angle ≈ 69.94 degrees
Therefore, the angle that the roof makes with the floor is approximately 70 degrees.
To find the angle that the roof makes with the floor of an A-frame house, you can use trigonometry.
First, let's draw a diagram to visualize the situation.
```
/|
/ |
/ |
/ |
/θ |
/ |
/______|
Width
```
In this diagram, the height of the A-frame house is 40 feet and the width is 30 feet. We need to find the angle, θ, which is the angle between the roof and the floor.
To find θ, we can use the tangent ratio:
```
tan(θ) = Opposite/Adjacent
```
In this case, the height of the house is the opposite side and the width is the adjacent side. So, we have:
```
tan(θ) = 40/30
```
To solve for θ, we can take the inverse tangent (also known as arctan) of both sides:
```
θ = arctan(40/30)
```
Now, let's calculate the value of θ using a calculator or computer:
```
θ ≈ arctan(40/30) ≈ 53.13 degrees
```
Therefore, the angle that the roof makes with the floor is approximately 53 degrees rounded to the nearest degree.