# Chapter 5 - Section 5.2 - Sum and Difference Formulas - Exercise Set - Page 671: 107

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

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