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Determine which is steeper.

Roof [tex]$A$[/tex] with a pitch of 1 in 5.5
Roof [tex]$B$[/tex] with a slope of [tex]$\frac{2}{13}$[/tex]

A. Roof A
B. Roof B
C. Neither

Sagot :

GinnyAnsweridn
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]
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