To find the horizontal distance from the base of the tower to where the zip line ends, we can use trigonometry. We have a right triangle where:
- The height of the zipline (the opposite side) is 120 feet.
- The angle of elevation (θ) is 65°.
- The horizontal distance (adjacent side) is what we want to find.
Using the tangent function, which relates the opposite side to the adjacent side in a right triangle, we have:
\[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} \]
This can be rearranged to find the adjacent side:
\[ \text{adjacent} = \frac{\text{opposite}}{\tan(θ)} \]
Plugging in the known values:
\[ \text{adjacent} = \frac{120}{\tan(65°)} \]
Now, calculate \(\tan(65°)\):
\[ \tan(65°) \approx 2.1445 \]
Now plug this into the equation:
\[ \text{adjacent} = \frac{120}{2.1445} \approx 55.9 \text{ feet} \]
Rounding this to the nearest whole number, the horizontal distance is approximately 56 feet.
So the correct response is 56 ft.