Question

The diagram shows the design of a house roof. Each side of the roof is 24 feet as shown, in the diagram. Use the Pythagorean theorem to answer each part. a) What is the approximate width of the house? Answer: The width of the house is 33.94 feet. b) What is the approximate height of the roof above the ceiling?

Answer 1

Given:

Find:(a) Approximate width "w" of house.

(B) Approximate Height of roof.

Sol:.

(a) Use Pythagorean theorm:

`\text{Hypotenuse}^2=base^2+perpendicular^2`
`\begin{gathered} \text{Hypotenuse}=w \\ \text{Base}=\text{ 24} \\ \text{perpendicular =24} \end{gathered}`
`\begin{gathered} w^2=24^2+24^2 \\ w^2=576+576 \\ w^2=1152 \\ w=\sqrt[]{1152} \\ w=33.94 \end{gathered}`

(b)

For "h"

Perpendicular = h

Base = w/2

Hypotenuse = 24

Use pythagorean theorm

`\begin{gathered} \text{Hypotenuse}^2=\text{Perpendicular}^2+\text{base}^2 \\ 24^2=h^2+((w)/(2))^2 \\ 24^2=h^2+(w^2)/(4) \\ 576=h^2+(1152)/(4) \\ 576-288=h^2 \\ h^2=288 \\ h=\sqrt[]{288} \\ h=16.97 \end{gathered}`

So the height is 16.97