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The problem asks for the rise of a roof, given that the pitch is 2:12 and the run is 20 feet.

### Step-by-step Solution:

1. **Understanding the pitch**:  
   The pitch of a roof, given as 2:12, means that for every 12 feet of horizontal distance (run), the roof rises 2 feet vertically (rise).

2. **Setting up the proportion**:  
   The pitch gives us a ratio:  
   \[
   \frac{\text{Rise}}{\text{Run}} = \frac{2}{12}
   \]
   
   We are given that the run is 20 feet. Let's call the rise \( x \). Therefore, we set up the proportion:
   \[
   \frac{x}{20} = \frac{2}{12}
   \]

3. **Solving the proportion**:  
   Cross-multiply to solve for \( x \):
   \[
   12x = 2 \times 20
   \]
   \[
   12x = 40
   \]
   \[
   x = \frac{40}{12} = 3.33 \text{ feet}
   \]

### Conclusion:
The rise of the roof is approximately 3.33 feet.

Would you like more details or have any further questions?

Here are 5 related questions for deeper understanding:
1. What is the relationship between pitch and angle of inclination in degrees?
2. How would the rise change if the pitch were steeper, say 4:12?
3. Can the pitch ratio be converted to a slope percentage? How?
4. How do you calculate the length of the roof's slope (the hypotenuse)?
5. What if the run were different, say 30 feet—how would the rise change?

**Tip:** Roof pitch is essential for calculating proper water drainage and structural load-bearing for various roofing materials.

If the pitch of a roof is supposed to be 2:12 and the run is 20 ft, what must be the rise?

Learn how to calculate the rise of a roof with a pitch of 2:12 and a run of 20 feet. This problem involves proportions and ratio concepts, suitable for students in Grades 6-8. Detailed solution provided.

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