Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Title: Finding the Slope of a Ramp**
**Objective:**
Learn how to calculate the slope of a ramp using the given dimensions.
**Introduction:**
The slope of a ramp is essential in determining how steep the incline is. Understanding how to calculate the slope can be useful in various real-life situations, such as constructing wheelchair ramps, roads, or walkways.
**Problem Statement:**
Find the slope of the ramp pictured below.
**Diagram Description:**
The diagram shows a right triangle formed by a ramp. The base of the triangle (the horizontal distance from the start of the ramp to the point directly below the top of the ramp) is labeled as 100 feet. The height of the triangle (the vertical rise from the base to the top of the ramp) is labeled as 12 feet.
**Detailed Analysis:**
1. The bottom of the ramp (horizontal side of the triangle) measures 100 feet.
2. The height (vertical side of the triangle) of the ramp measures 12 feet.
**Definition of Slope:**
The slope of a line or ramp is calculated as the rise over the run (vertical change divided by horizontal change).
**Calculation:**
To find the slope (m) of the ramp, use the formula:
\[ \text{Slope} (m) = \frac{\text{Rise}}{\text{Run}} \]
For this ramp:
- Rise = 12 feet
- Run = 100 feet
So,
\[ \text{Slope} (m) = \frac{12 \, \text{feet}}{100 \, \text{feet}} \]
\[ \text{Slope} (m) = 0.12 \]
**Conclusion:**
The slope of the ramp is 0.12. This means that for every 100 feet of horizontal distance, the ramp rises 12 feet. This gentle incline is appropriate for various accessibility needs, ensuring a practical and safe slope for movement.
**Practice Problem:**
Use the given dimensions of a ramp where the horizontal distance is 150 feet and the vertical rise is 15 feet. Calculate the slope.
\[ \text{Solution:} \text{Slope} (m) = \frac{15 \, \text{feet}}{150 \, \text{feet}} = 0.10 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F902e7e06-dd9d-47fe-961b-7a721406cdf1%2F42a23931-17f8-4d0c-8a6a-48cd7b0cb904%2Fz7qgcc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Finding the Slope of a Ramp**
**Objective:**
Learn how to calculate the slope of a ramp using the given dimensions.
**Introduction:**
The slope of a ramp is essential in determining how steep the incline is. Understanding how to calculate the slope can be useful in various real-life situations, such as constructing wheelchair ramps, roads, or walkways.
**Problem Statement:**
Find the slope of the ramp pictured below.
**Diagram Description:**
The diagram shows a right triangle formed by a ramp. The base of the triangle (the horizontal distance from the start of the ramp to the point directly below the top of the ramp) is labeled as 100 feet. The height of the triangle (the vertical rise from the base to the top of the ramp) is labeled as 12 feet.
**Detailed Analysis:**
1. The bottom of the ramp (horizontal side of the triangle) measures 100 feet.
2. The height (vertical side of the triangle) of the ramp measures 12 feet.
**Definition of Slope:**
The slope of a line or ramp is calculated as the rise over the run (vertical change divided by horizontal change).
**Calculation:**
To find the slope (m) of the ramp, use the formula:
\[ \text{Slope} (m) = \frac{\text{Rise}}{\text{Run}} \]
For this ramp:
- Rise = 12 feet
- Run = 100 feet
So,
\[ \text{Slope} (m) = \frac{12 \, \text{feet}}{100 \, \text{feet}} \]
\[ \text{Slope} (m) = 0.12 \]
**Conclusion:**
The slope of the ramp is 0.12. This means that for every 100 feet of horizontal distance, the ramp rises 12 feet. This gentle incline is appropriate for various accessibility needs, ensuring a practical and safe slope for movement.
**Practice Problem:**
Use the given dimensions of a ramp where the horizontal distance is 150 feet and the vertical rise is 15 feet. Calculate the slope.
\[ \text{Solution:} \text{Slope} (m) = \frac{15 \, \text{feet}}{150 \, \text{feet}} = 0.10 \]
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