Question

Find the length of the sloping side of the roof. Give your answer to the nearest foot. Show your work.

Answer 1

Given:

The triangle having two similar angles.

This is the isosceles traingle.

Draw the altitude to the given traingle,

D divides the side BC into two equal side having length,

`\begin{gathered} (45)/(2)=22.5 \\ BD=22.5\text{ and DC=22.5} \end{gathered}`

Now, use the tan ratio for right triangle ABD,

`\begin{gathered} tan15^(\circ)=(AD)/(BD) \\ 0.268=(AD)/(22.5) \\ AD=6.02=6\text{ f}eet \end{gathered}`

Using the pythagorean theorem,

`\begin{gathered} AB^2=AD^2+BD^2 \\ =6^2+22.5^2 \\ =542.25 \\ =23.286 \\ =23.3 \end{gathered}`

The length of the sloping side of the roof is 23.3 feet.