Answer
The balloon rises $138.8$ feet.
Work Step by Step
Let the heights of the balloon for elevations of $37.1{}^\circ $ and $62.4{}^\circ $ be ${{H}_{1}}$ and ${{H}_{2}}$ , respectively.
Thus, the increase in balloon height $={{H}_{2}}-{{H}_{1}}$
$\tan \left( 37.1{}^\circ \right)=\frac{{{H}_{1}}}{120}$
Then,
$\tan \left( 62.4{}^\circ \right)=\frac{{{H}_{2}}}{120}$
So,
$\begin{align}
& {{H}_{2}}-{{H}_{1}}\text{=120}\left( \text{tan}\left( \text{62}\text{.4}{}^\circ \right)-\text{tan}\left( \text{37}\text{.1}{}^\circ \right) \right) \\
& \quad \quad \quad \text{=138}\text{.78 feet} \\
\end{align}$
Hence, the balloon rises $138.8$ feet
