Question

A zipline starts 120
feet above the ground and covers a diagonal distance, forming a triangle with the ground. If the angle of elevation where the zip line meets the ground is 65°
, what is the horizontal distance from the base of the tower to where the zip line ends?(1 point)
Responses

Answer 1

To find the horizontal distance from the base of the tower to where the zip line ends, we can use the tangent of the angle of elevation in a right triangle. In this case:

- The height of the zipline (opposite side) is 120 feet.
- The angle of elevation is 65°.
- The horizontal distance (adjacent side) is what we are solving for.

We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side:

\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]

Plugging in our values:

\[
\tan(65^\circ) = \frac{120}{d}
\]

where \(d\) is the horizontal distance. Rearranging the equation to solve for \(d\):

\[
d = \frac{120}{\tan(65^\circ)}
\]

Now we calculate \(\tan(65^\circ)\):

Using a calculator:

\(\tan(65^\circ) \approx 2.1445\)

Now plugging this value back into our equation:

\[
d \approx \frac{120}{2.1445} \approx 55.9
\]

Therefore, the horizontal distance from the base of the tower to where the zip line ends is approximately **55.9 feet**.