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Word Problems with Right Triangles

Suppose you stand at the top of a ski slope and look down to the bottom. The angle of depression and elevation/height of slope is given. Find the distance ( $d$ ) a person must travel to get to the bottom of the slope.

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$\begin{equation*} 90^\circ - 22^\circ = 68^\circ \end{equation*}$

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$\begin{equation*} \cos(\theta) = \frac{\text{adj}}{\text{hyp}} \end{equation*}$

$\begin{equation*} d \cdot \cos \left( 68^\circ \right) = \left( \frac{482 \text{ ft}}{d} \right) \cdot d \end{equation*}$

$\begin{equation*} d \cdot \cos \left( 68^\circ \right) = 482 \end{equation*}$

$\begin{equation*} \frac{d \cdot \cos \left( 68^\circ \right)}{\cos \left( 68^\circ \right)} = \frac{482}{\cos \left( 68^\circ \right)} \end{equation*}$

$\begin{equation*} d = \frac{482}{\cos \left( 68^\circ \right)} \end{equation*}$

$\begin{equation*} d = \frac{482}{0.375} \end{equation*}$

$\begin{equation*} \boxed{d = 1285.3 \text{ ft}} \end{equation*}$