To find the horizontal distance (x) 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 tangent function which is defined as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this context, the "opposite" side is the vertical height (25 feet), and the "adjacent" side is the horizontal distance (x).
So, we have:
\[ \tan(27°) = \frac{25}{x} \]
Now we can solve for \(x\):
\[ x = \frac{25}{\tan(27°)} \]
Calculating \(\tan(27°)\):
\[ \tan(27°) \approx 0.5095 \]
Now substitute this back into the equation for \(x\):
\[ x \approx \frac{25}{0.5095} \approx 49.07 \]
Thus, the horizontal distance \( x \) the zipline will cover is approximately 49.07 ft.
The correct choice is:
x = 49.07 ft.