To find the horizontal distance from the base of the tower to where the zip line ends, we can use some basic trigonometry. In this case, we can use the tangent function since we know the angle of elevation and the height of the zipline.
The tangent of an angle in a right triangle is given by the formula:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In this case, the opposite side is the height of the zip line (120 feet), and the adjacent side is the horizontal distance \(d\) that we want to find. Thus, we can rewrite the tangent as:
\[ \tan(65°) = \frac{120 \text{ ft}}{d} \]
Rearranging to solve for \(d\):
\[ d = \frac{120 \text{ ft}}{\tan(65°)} \]
Now, let's calculate \(\tan(65°)\):
\[ \tan(65°) \approx 2.1445 \]
Now plug this back into the equation:
\[ d \approx \frac{120 \text{ ft}}{2.1445} \approx 55.9 \text{ ft} \]
Rounding to the nearest whole number, the horizontal distance \(d\) is approximately 56 ft.
Therefore, the answer is:
56 ft.
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