To find the horizontal distance \( x \) that the zipline will cover, we can use trigonometry, specifically the tangent function. Given that the height of the zipline is 25 feet and the angle of elevation is 27°, we can use the following relationship:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, the opposite side is the height of the zipline (25 feet) and the adjacent side is the horizontal distance \( x \). Therefore, we can set up the equation:
\[ \tan(27°) = \frac{25}{x} \]
To solve for \( x \), we can rearrange this equation:
\[ x = \frac{25}{\tan(27°)} \]
Now, we need to calculate \( \tan(27°) \):
\[ \tan(27°) \approx 0.5095 \]
Now plug this value into the equation:
\[ x = \frac{25}{0.5095} \approx 49.1 \text{ feet} \]
Thus, the horizontal distance the zipline will cover is approximately 49.1 feet.
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