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 (opposite side) = 120 feet
- The angle of elevation = 65°
- The horizontal distance (adjacent side) = ?
Using the tangent function, which relates the opposite side to the adjacent side, we have:
\[ \tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}} \]
Substituting the values we know:
\[ \tan(65°) = \frac{120 \text{ ft}}{\text{horizontal distance}} \]
Let \( x \) be the horizontal distance:
\[ \tan(65°) = \frac{120}{x} \]
Now rearranging the equation to solve for \( x \):
\[ x = \frac{120}{\tan(65°)} \]
Using a calculator to find \( \tan(65°) \):
\[ \tan(65°) \approx 2.1445 \]
Now substituting back into the equation:
\[ x \approx \frac{120}{2.1445} \approx 55.9 \text{ ft} \]
Rounding this value, we find:
\[ x \approx 56 \text{ ft} \]
Therefore, the horizontal distance from the base of the tower to where the zip line ends is approximately 56 ft.
The correct answer is:
- 56 ft.