Answer
The ship is approx $357\text{ feet}$ from the lighthouse and the plane is approx $394\text{ feet}$ above the water.
Work Step by Step
Let us assume a = distance of the ship from the lighthouse.
$\tan {{35}^{0}}=\frac{250}{a}\approx 357$
And the ship is approximately 357 feet from the lighthouse.
Let b = plane's height above the lighthouse
$\begin{align}
& \tan {{22}^{0}}=\frac{357}{b} \\
& b=357\tan {{22}^{0}}=357\left( 0.404 \right)\approx 144 \\
& 144+357=394
\end{align}$
Thus, the plane is approximately $394feet$ above the water.
