Question
tan (0) = height/length - 24 inches/28 inches
tan(0)=24/288=1/12
0=tan -1 (1/12)
0 = 4.76
height of the door abouve ground level is 24 inches
ramp angle : 4.76 degrees
On a separate sheet of paper, provide a rough sketch of the ramp or ramp
sections with labeled horizontal run, vertical rise, ramp length, and angle that
the ramp makes with the ground. Below your sketch, include the calculations
you made to determine the horizontal run and vertical rise of your ramp.
Round all final answers to the nearest tenth.
tan(0)=24/288=1/12
0=tan -1 (1/12)
0 = 4.76
height of the door abouve ground level is 24 inches
ramp angle : 4.76 degrees
On a separate sheet of paper, provide a rough sketch of the ramp or ramp
sections with labeled horizontal run, vertical rise, ramp length, and angle that
the ramp makes with the ground. Below your sketch, include the calculations
you made to determine the horizontal run and vertical rise of your ramp.
Round all final answers to the nearest tenth.
Answers
Answered by
GPT-4o mini
Here's a breakdown of the sketch and calculations based on the information provided about the ramp.
### Sketch Description
1. **Ramp Sketch**: Draw a right triangle where:
- The **vertical rise** (height of the door) is labeled as **24 inches** (from the ground to the top of the door).
- The **horizontal run** (distance from the bottom of the ramp to the wall) is labeled as **28 inches**.
- The **ramp length** (hypotenuse) should be labeled.
2. **Angle**: Mark the angle between the ground and the ramp, labeled as approximately **4.76 degrees**.
### Calculations
#### Given Values:
- Height of the door (Vertical rise, \( h \)): 24 inches
- Length of the run (Horizontal run, \( r \)): 28 inches
- Ramp angle (\( \theta \)): 4.76 degrees
#### 1. Calculating Ramp Length
To find the length of the ramp (\( L \)), use the Pythagorean theorem:
\[
L = \sqrt{h^2 + r^2}
\]
\[
L = \sqrt{(24)^2 + (28)^2}
\]
Calculating:
\[
L = \sqrt{576 + 784} = \sqrt{1360} \approx 36.9 \text{ inches}
\]
#### Results:
- **Vertical Rise (Height)**: 24 inches
- **Horizontal Run**: 28 inches
- **Ramp Length**: 36.9 inches
- **Angle with the ground**: 4.76 degrees
### Final Round Numbers
- Height of ramp: **24.0 inches** (rounded to the nearest tenth)
- Horizontal run: **28.0 inches** (rounded to the nearest tenth)
- Ramp length: **36.9 inches** (already to the nearest tenth)
- Ramp angle: **4.8 degrees** (rounded to the nearest tenth)
### Summary
In your final sketch, the ramp's height (24 inches), horizontal distance (28 inches), and hypotenuse length (36.9 inches) should be visually represented, alongside the angle calculated, and all dimensions labeled clearly. Note that the angle you noted as “4.76 degrees” can be rounded to **4.8 degrees** for clarity, specifying that all values are rounded to one decimal place.
### Sketch Description
1. **Ramp Sketch**: Draw a right triangle where:
- The **vertical rise** (height of the door) is labeled as **24 inches** (from the ground to the top of the door).
- The **horizontal run** (distance from the bottom of the ramp to the wall) is labeled as **28 inches**.
- The **ramp length** (hypotenuse) should be labeled.
2. **Angle**: Mark the angle between the ground and the ramp, labeled as approximately **4.76 degrees**.
### Calculations
#### Given Values:
- Height of the door (Vertical rise, \( h \)): 24 inches
- Length of the run (Horizontal run, \( r \)): 28 inches
- Ramp angle (\( \theta \)): 4.76 degrees
#### 1. Calculating Ramp Length
To find the length of the ramp (\( L \)), use the Pythagorean theorem:
\[
L = \sqrt{h^2 + r^2}
\]
\[
L = \sqrt{(24)^2 + (28)^2}
\]
Calculating:
\[
L = \sqrt{576 + 784} = \sqrt{1360} \approx 36.9 \text{ inches}
\]
#### Results:
- **Vertical Rise (Height)**: 24 inches
- **Horizontal Run**: 28 inches
- **Ramp Length**: 36.9 inches
- **Angle with the ground**: 4.76 degrees
### Final Round Numbers
- Height of ramp: **24.0 inches** (rounded to the nearest tenth)
- Horizontal run: **28.0 inches** (rounded to the nearest tenth)
- Ramp length: **36.9 inches** (already to the nearest tenth)
- Ramp angle: **4.8 degrees** (rounded to the nearest tenth)
### Summary
In your final sketch, the ramp's height (24 inches), horizontal distance (28 inches), and hypotenuse length (36.9 inches) should be visually represented, alongside the angle calculated, and all dimensions labeled clearly. Note that the angle you noted as “4.76 degrees” can be rounded to **4.8 degrees** for clarity, specifying that all values are rounded to one decimal place.