$1.$ Draw a picture. Let $b$ be the current (broken) height of the tree, that is, the distance from the ground to the break, which is really only a sharp bend. Then $\frac{b}{20}=\tan(50^\circ).$ Let $\ell$ be the length of the "leaning" part. Then $\frac{20}{\ell}=\cos(50^\circ).$ Finally, the original height of the tree is $b+\ell$.
The calculation: We have $b=20\tan(50^\circ)\approx 23.835$, and $\ell=\frac{20}{\cos(50^\circ)}\approx 31.114$, giving a sum of $\approx 54.95$.
$2.$ Draw a picture. Let $O$ be the point of intersection of the streets, $G$ the gas station, and $P$ the point on the other road nearest to the gas station. Then $\angle OPG$ is a right angle. Thus $\frac{PG}{OG}=\sin(75^\circ).$
The calculator gives the distance as approximately $965.9$. Presumably you have instructions about what kind of rounding to do.