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)
• x = 135.10 ft.
• x = 29.38 ft.
• x = 12.74 ft.
• x = 49.07 ft.

Answer 1

To find the horizontal distance \( x \) that the zipline covers, we can use the relationship defined by the angle of elevation, the height of the starting point, and the horizontal distance.

Given:
- Height \( h = 25 \) feet
- Angle of elevation \( \theta = 27^\circ \)

Using the tangent function, which relates the opposite side (height) to the adjacent side (horizontal distance), we have:

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

Rearranging the equation to solve for \( x \):

\[
x = \frac{h}{\tan(\theta)}
\]

Substituting the known values:

\[
x = \frac{25}{\tan(27^\circ)}
\]

Now we calculate \( \tan(27^\circ) \) using a calculator:

\[
\tan(27^\circ) \approx 0.5095
\]

Now substitute this value into the equation:

\[
x = \frac{25}{0.5095} \approx 49.07 \text{ feet}
\]

Based on this calculation, the horizontal distance the zipline will cover is:

\[
\boxed{49.07 \text{ ft.}}
\]