Question

A zipline starts 25 feet off the ground and has an angle of elevation of 27° . What is the horizontal distance the zipline will cover, x?(1 point)
Responses

Answer 1

To find the horizontal distance \( x \) that 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 following relationship:

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

In this case, the opposite side is the height of the zipline (25 feet) and the adjacent side is the horizontal distance \( x \). Therefore, we can set up the equation:

\[
\tan(27°) = \frac{25}{x}
\]

To solve for \( x \), we can rearrange this equation:

\[
x = \frac{25}{\tan(27°)}
\]

Now, we need to calculate \( \tan(27°) \):

\[
\tan(27°) \approx 0.5095
\]

Now plug this value into the equation:

\[
x = \frac{25}{0.5095} \approx 49.1 \text{ feet}
\]

Thus, the horizontal distance the zipline will cover is approximately **49.1 feet**.