Question

An A-frame house is 40 feet high and 25 feet wide. Find the measure ofthe angle that the roof makes with the floor. Round to the nearest degree.

Answer 1

STEP 1

Interpretation of question in geometric terms.

This will require us to diagrammatically depict the question and assign the house with a conventional geometric shape

In the above shape, we have successfully made a right angled triangle of our scenario and can now move to 2nd step.

STEP 2

We will use the Soh Cah Toa notation to solve for angle x where:

`\begin{gathered} \text{Tan x = }(opp)/(adj)\text{ where} \\ \text{adjacent = }(25)/(2)=12.5\text{ ft} \\ \text{opposite = }40\text{ ft} \end{gathered}`

Therefore,

`T\text{an x = }(opp)/(adj)\text{ = }(40)/(12.5)=3.2`
`x=\text{Tan}^(-1)3.2=72.6`

Therefore, the angle the roof makes with the floor is 73 degrees