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.
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.
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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![**Educational Website Content - Trigonometry Applied in Real-Life Situations: Calculating the Length of a Wheelchair Ramp**
**Question:**
How long should a wheelchair ramp be if the angle of incline is to be 33 degrees and the vertical end of the ramp is to be 3 feet high? Round to the nearest tenth.
**Answer Choices:**
- A) 3.6 ft
- B) 1.6 ft
- C) 5.5 ft
- D) 4.6 ft
**Explanation:**
To determine the length of the wheelchair ramp, we need to apply trigonometric principles, specifically the sine function, which relates the angle of incline to the opposite side (the height) and the hypotenuse (the ramp length). The sine function is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Where:
- \(\theta\) is the angle of incline (33 degrees)
- The opposite side is the vertical height of the ramp (3 feet)
- The hypotenuse is the length of the ramp we need to find
Rearranging the equation to solve for the hypotenuse (ramp length), we get:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the known values:
\[ \text{hypotenuse} = \frac{3\text{ ft}}{\sin(33^\circ)} \]
Using a calculator to find \(\sin(33^\circ)\):
\[ \sin(33^\circ) \approx 0.5446 \]
Thus:
\[ \text{hypotenuse} = \frac{3}{0.5446} \approx 5.5 \text{ ft} \]
**Correct Answer:**
- C) 5.5 ft
This demonstrates how trigonometric functions can be used to solve practical problems such as designing wheelchair ramps.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c67c4d0-217c-4e3e-983c-7902447cdce8%2F75eab21a-0122-47ba-b184-a5a9a0b7e705%2Fh11vui8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content - Trigonometry Applied in Real-Life Situations: Calculating the Length of a Wheelchair Ramp**
**Question:**
How long should a wheelchair ramp be if the angle of incline is to be 33 degrees and the vertical end of the ramp is to be 3 feet high? Round to the nearest tenth.
**Answer Choices:**
- A) 3.6 ft
- B) 1.6 ft
- C) 5.5 ft
- D) 4.6 ft
**Explanation:**
To determine the length of the wheelchair ramp, we need to apply trigonometric principles, specifically the sine function, which relates the angle of incline to the opposite side (the height) and the hypotenuse (the ramp length). The sine function is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Where:
- \(\theta\) is the angle of incline (33 degrees)
- The opposite side is the vertical height of the ramp (3 feet)
- The hypotenuse is the length of the ramp we need to find
Rearranging the equation to solve for the hypotenuse (ramp length), we get:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the known values:
\[ \text{hypotenuse} = \frac{3\text{ ft}}{\sin(33^\circ)} \]
Using a calculator to find \(\sin(33^\circ)\):
\[ \sin(33^\circ) \approx 0.5446 \]
Thus:
\[ \text{hypotenuse} = \frac{3}{0.5446} \approx 5.5 \text{ ft} \]
**Correct Answer:**
- C) 5.5 ft
This demonstrates how trigonometric functions can be used to solve practical problems such as designing wheelchair ramps.
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