rafter rise The pitch of a roof is defined as and the fraction is typically written with a denominator of 12. Determine the rafter run pitch of the roof from point A to point C. Rafter 7 ft Span 24 ft
rafter rise The pitch of a roof is defined as and the fraction is typically written with a denominator of 12. Determine the rafter run pitch of the roof from point A to point C. Rafter 7 ft Span 24 ft
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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![### Roof Pitch Calculation
**Question:**
The pitch of a roof is defined as \( \frac{\text{rafter rise}}{\text{rafter run}} \) and the fraction is typically written with a denominator of 12. Determine the pitch of the roof from point A to point C.
**Diagram:**
- A diagram is displayed with the following details:
- There is a triangle representing the roof structure.
- Point A is at the bottom left of the triangle, point B is at the bottom right, and point C is at the top center.
- The segment labeled "Span 24 ft" represents the distance between points A and B at the base of the triangle.
- The segment labeled "7 ft" represents the vertical height from the base to the peak of the roof, from point C to the midpoint of AB.
**Graph Explanation:**
- This graph shows a right triangle with a base (AB) spanning 24 feet and a height (vertical rise from the base to the peak of the roof, point C) of 7 feet.
- The rafter AC and rafter BC are represented as the hypotenuse of the two right triangles formed by splitting the main triangle into two smaller right triangles.
### Steps to Determine Roof Pitch:
1. **Identify the rafter run:** The rafter run in this case is half of the span. Therefore, the rafter run is \( \frac{24 \text{ ft}}{2} = 12 \text{ ft} \).
2. **Identify the rafter rise:** The rafter rise is given as 7 ft.
3. **Calculate the pitch:**
\[
\text{Pitch} = \frac{\text{rafter rise}}{\text{rafter run}} = \frac{7 \text{ ft}}{12 \text{ ft}}
\]
Therefore, the pitch of the roof from point A to point C is \( \frac{7}{12} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a2625eb-f481-4d8b-8f1d-c99144b45fbd%2F405fd65c-30b3-4aad-925d-d738425d3a14%2F162b3ko_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Roof Pitch Calculation
**Question:**
The pitch of a roof is defined as \( \frac{\text{rafter rise}}{\text{rafter run}} \) and the fraction is typically written with a denominator of 12. Determine the pitch of the roof from point A to point C.
**Diagram:**
- A diagram is displayed with the following details:
- There is a triangle representing the roof structure.
- Point A is at the bottom left of the triangle, point B is at the bottom right, and point C is at the top center.
- The segment labeled "Span 24 ft" represents the distance between points A and B at the base of the triangle.
- The segment labeled "7 ft" represents the vertical height from the base to the peak of the roof, from point C to the midpoint of AB.
**Graph Explanation:**
- This graph shows a right triangle with a base (AB) spanning 24 feet and a height (vertical rise from the base to the peak of the roof, point C) of 7 feet.
- The rafter AC and rafter BC are represented as the hypotenuse of the two right triangles formed by splitting the main triangle into two smaller right triangles.
### Steps to Determine Roof Pitch:
1. **Identify the rafter run:** The rafter run in this case is half of the span. Therefore, the rafter run is \( \frac{24 \text{ ft}}{2} = 12 \text{ ft} \).
2. **Identify the rafter rise:** The rafter rise is given as 7 ft.
3. **Calculate the pitch:**
\[
\text{Pitch} = \frac{\text{rafter rise}}{\text{rafter run}} = \frac{7 \text{ ft}}{12 \text{ ft}}
\]
Therefore, the pitch of the roof from point A to point C is \( \frac{7}{12} \).
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