To find the horizontal distance \( x \) that the zipline covers, we can use the relationship defined by the angle of elevation, the height of the starting point, and the horizontal distance.
Given:
- Height \( h = 25 \) feet
- Angle of elevation \( \theta = 27^\circ \)
Using the tangent function, which relates the opposite side (height) to the adjacent side (horizontal distance), we have:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{x} \]
Rearranging the equation to solve for \( x \):
\[ x = \frac{h}{\tan(\theta)} \]
Substituting the known values:
\[ x = \frac{25}{\tan(27^\circ)} \]
Now we calculate \( \tan(27^\circ) \) using a calculator:
\[ \tan(27^\circ) \approx 0.5095 \]
Now substitute this value into the equation:
\[ x = \frac{25}{0.5095} \approx 49.07 \text{ feet} \]
Based on this calculation, the horizontal distance the zipline will cover is:
\[ \boxed{49.07 \text{ ft.}} \]
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