To determine which roof is steeper, we need to compare the slopes of the two roofs.
First, we find the slope of Roof A. The pitch of Roof A is given as 1 in 5.5. This means that for every 5.5 units of horizontal distance, Roof A rises by 1 unit. The slope, therefore, can be calculated as:
[tex]\[ \text{slope}_A = \frac{1}{5.5} = 0.18181818181818182 \][/tex]
Next, we consider Roof B, which has a slope given directly as [tex]\(\frac{2}{13}\)[/tex]. This means the slope is:
[tex]\[ \text{slope}_B = \frac{2}{13} = 0.15384615384615385 \][/tex]
Now we compare the two slopes:
- Slope of Roof A: 0.18181818181818182
- Slope of Roof B: 0.15384615384615385
Since 0.18181818181818182 (slope of Roof A) is greater than 0.15384615384615385 (slope of Roof B), Roof A is steeper than Roof B.
Therefore, the steeper roof is:
[tex]\[ \boxed{\text{Roof A}} \][/tex]
