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,
[tex]\begin{gathered} \frac{45}{2}=22.5 \\ BD=22.5\text{ and DC=22.5} \end{gathered}[/tex]
Now, use the tan ratio for right triangle ABD,
[tex]\begin{gathered} tan15^{\circ}=\frac{AD}{BD} \\ 0.268=\frac{AD}{22.5} \\ AD=6.02=6\text{ f}eet \end{gathered}[/tex]
Using the pythagorean theorem,
[tex]\begin{gathered} AB^2=AD^2+BD^2 \\ =6^2+22.5^2 \\ =542.25 \\ =23.286 \\ =23.3 \end{gathered}[/tex]
The length of the sloping side of the roof is 23.3 feet.
