Answer
The value of $h=699.1$.
Work Step by Step
In the given graph
$\begin{align}
& \angle ABC=180{}^\circ -29{}^\circ \\
& =151{}^\circ \\
& \angle ACB=180{}^\circ -25{}^\circ -151{}^\circ \\
& =4{}^\circ
\end{align}$
Using the law of sines, we will find $\overline{BC}$
$\begin{align}
& \frac{\overline{BC}}{\sin 25{}^\circ }=\frac{238}{\sin 4{}^\circ } \\
& \overline{BC}=\frac{238\sin 25{}^\circ }{\sin 4{}^\circ } \\
& \overline{BC}\approx 1441.9
\end{align}$
Now, using the law of sines, we will find h.
$\begin{align}
& \frac{h}{\sin 29{}^\circ }=\frac{1441.9}{\sin 90{}^\circ } \\
& h=\frac{1441.9\sin 29{}^\circ }{\sin 90{}^\circ } \\
& h\approx 699.1
\end{align}$
