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 which answer is correct and why

x=29.38 ft.
x equals 29.38 ft.

x=135.10 ft.
x equals 135.10 ft.

x=12.74 ft.
x equals 12.74 ft.

x=49.07 ft.

Answer 1

To determine the horizontal distance \( x \) that the zipline will cover, we can use trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of the right triangle formed by the zipline.

In this case:

- The height of the zipline (opposite side) is 25 feet.
- The angle of elevation is 27°.
- The horizontal distance (adjacent side) is \( x \).

Using the tangent function, we have:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{25}{x}
\]

Substituting the known values:

\[
\tan(27°) = \frac{25}{x}
\]

To find \( x \), we can rearrange the equation:

\[
x = \frac{25}{\tan(27°)}
\]

Now, we calculate \( \tan(27°) \):

Using a calculator:

\[
\tan(27°) \approx 0.5108
\]

Now substituting back into the equation for \( x \):

\[
x = \frac{25}{0.5108} \approx 48.96 \text{ feet}
\]

Rounding to two decimal places, we can say:

\[
x \approx 49.07 \text{ feet}
\]

Therefore, the correct response is:

**x = 49.07 ft.**