How long should a wheel chair ramp be if the angle of incline is to be 33° and the vertical end of the ramp is to be 3 feet high? Round to the nearest tenth. 4.6 ft 1.6 ft 3.6 ft 5.5 ft A
How long should a wheel chair ramp be if the angle of incline is to be 33° and the vertical end of the ramp is to be 3 feet high? Round to the nearest tenth. 4.6 ft 1.6 ft 3.6 ft 5.5 ft A
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Wheelchair Ramp Calculation
**Question:**
How long should a wheelchair ramp be if the angle of incline is to be 33° and the vertical end of the ramp is to be 3 feet high? Round to the nearest tenth.
**Options:**
A. 4.6 ft
B. 1.6 ft
C. 3.6 ft
D. 5.5 ft
This problem involves calculating the length of a ramp using trigonometric principles. Specifically, it requires using the sine function to determine the length of the hypotenuse of a right triangle, where:
- The angle of incline (θ) = 33°
- The height (opposite side) = 3 feet
Using the formula:
\[ \text{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
We solve for the hypotenuse:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\text{sin}(\theta)} \]
\[ \text{hypotenuse} = \frac{3}{\text{sin}(33°)} \]
After calculating, choose the option closest to your result as the length of the ramp.
Identify the correct answer from the options given based on your computations.
**Explanation of Options:**
- **Option A: 4.6 ft** - This length may represent a ramp possibly conforming to accessibility standards.
- **Option B: 1.6 ft** - This length implies a very steep ramp, which is impractical.
- **Option C: 3.6 ft** - This length is more moderate.
- **Option D: 5.5 ft** - This is longer and may suggest a shallower ramp.
Choose the most accurate length after solving the trigonometric equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af3b856-d446-4ff7-a63e-89e70c8da553%2Fc24244a6-8c28-47c7-a31b-d1336e125c68%2Fylw4bsn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Wheelchair Ramp Calculation
**Question:**
How long should a wheelchair ramp be if the angle of incline is to be 33° and the vertical end of the ramp is to be 3 feet high? Round to the nearest tenth.
**Options:**
A. 4.6 ft
B. 1.6 ft
C. 3.6 ft
D. 5.5 ft
This problem involves calculating the length of a ramp using trigonometric principles. Specifically, it requires using the sine function to determine the length of the hypotenuse of a right triangle, where:
- The angle of incline (θ) = 33°
- The height (opposite side) = 3 feet
Using the formula:
\[ \text{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
We solve for the hypotenuse:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\text{sin}(\theta)} \]
\[ \text{hypotenuse} = \frac{3}{\text{sin}(33°)} \]
After calculating, choose the option closest to your result as the length of the ramp.
Identify the correct answer from the options given based on your computations.
**Explanation of Options:**
- **Option A: 4.6 ft** - This length may represent a ramp possibly conforming to accessibility standards.
- **Option B: 1.6 ft** - This length implies a very steep ramp, which is impractical.
- **Option C: 3.6 ft** - This length is more moderate.
- **Option D: 5.5 ft** - This is longer and may suggest a shallower ramp.
Choose the most accurate length after solving the trigonometric equation.
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