Precalculus (6th Edition) Blitzer

$30.5\ ft$
The roof sides and ground form an isosceles triangle. Assume the side length is $x$ feet; we have $2x\ cos55=35$ which gives $x=\frac{35}{2cos55}\approx30.5\ ft$. You can also use the Laws of Sines for this problem by finding the third angle first.