Question

build your skills

1. the pitch of a roof on a lean - to that dianna is building is 2:5. if the lean - to touches the ground 4.8 m from the base of the building, how high up the building does it reach?
2. what is the pitch of the roof of an a - frame building if its height is 3.6 m and its width is 5.4 m?
3. the roof of a tool shed has a pitch of 2:5. if the shed is 7 feet wide, what is the rise of the roof?

Explanation:

Step1: Define pitch ratio

The pitch 2:5 means for every 5 units of horizontal run, there are 2 units of vertical rise. Let the height up the building be $h$. The horizontal run is 4.8 m.

Step2: Set up proportion

We set up the proportion $\frac{h}{4.8}=\frac{2}{5}$.

Step3: Solve for $h$

Cross - multiply: $5h = 4.8\times2$. Then $5h=9.6$. Divide both sides by 5: $h=\frac{9.6}{5}=1.92$ m.

for question 10:

Step1: Determine horizontal run for A - frame

For an A - frame, the horizontal run for one side is half of the width. So the horizontal run $x=\frac{5.4}{2}=2.7$ m and the vertical rise $y = 3.6$ m.

Step2: Find pitch ratio

The pitch is the ratio of the vertical rise to the horizontal run. The pitch ratio is $\frac{3.6}{2.7}=\frac{36}{27}=\frac{4}{3}$, so the pitch is 4:3.

for question 11:

Step1: Define pitch ratio and given values

The pitch 2:5 means for every 5 units of horizontal run, there are 2 units of vertical rise. The horizontal run for the shed (width) is 7 feet. Let the rise be $r$.

Step2: Set up proportion

We set up the proportion $\frac{r}{7}=\frac{2}{5}$.

Step3: Solve for $r$

Cross - multiply: $5r=7\times2$. Then $5r = 14$. Divide both sides by 5: $r=\frac{14}{5}=2.8$ feet.

Answer:

1.92 m