Question

find the pitch of a symmetrical roof for the given dimensions.

1. rise: 7.5 ft

span 11.25 ft

1. rise: 36 in

run: 32 in
find the rise of each roof. assume it is symmetrical.

1. span: 39 m

pitch: 1/3

1. run: 12 ft

pitch: 3/4

Explanation:

Step1: Recall pitch formula

The pitch of a roof is given by the ratio of the rise to the run. For a symmetrical roof, if given span, run = span/2.

Step2: Solve problem 1

Given rise = 7.5 ft and span = 11.25 ft. First, find the run. Run = span/2 = 11.25/2 = 5.625 ft. Then pitch = $\frac{7.5}{5.625}=\frac{7.5\times1000}{5.625\times1000}=\frac{7500}{5625}=\frac{2}{3}$.

Step3: Solve problem 2

Given rise = 36 in and run = 32 in. Pitch = $\frac{36}{32}=\frac{9}{8}$.

Step4: Solve problem 4

Given span = 39 m and pitch = $\frac{1}{3}$. Since run = span/2 = 19.5 m, and pitch = $\frac{rise}{run}$, then rise = pitch×run. So rise=$\frac{1}{3}\times19.5 = 13$ m.

Step5: Solve problem 5

Given run = 12 ft and pitch = $\frac{3}{4}$. Since pitch = $\frac{rise}{run}$, then rise = pitch×run. So rise=$\frac{3}{4}\times12 = 9$ ft.

Answer:

1. $\frac{2}{3}$
2. $\frac{9}{8}$
3. 13 m
4. 9 ft