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)

Question

Responses

x=49.07 ft.
x equals 49.07 ft.

x=135.10 ft.
x equals 135.10 ft.

x=12.74 ft.
x equals 12.74 ft.

x=29.38 ft.

Answer 1

To find the horizontal distance \( x \) covered by the zipline, we can use the tangent of the angle of elevation. The height of the zipline is 25 feet, and the angle of elevation is 27°.

The tangent function is defined as:

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

Here, the "opposite" side is the height (25 feet), and the "adjacent" side is the horizontal distance \( x \). Thus, we can set up the equation:

\[ \tan(27°) = \frac{25}{x} \]

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

\[ x = \frac{25}{\tan(27°)} \]

Now we can calculate \( x \):

1. Calculate \( \tan(27°) \): \[ \tan(27°) \approx 0.5108 \]

2. Substitute into the equation for \( x \): \[ x = \frac{25}{0.5108} \approx 48.94 \text{ feet} \]

Rounding this to two decimal places, we get approximately:

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

Thus, the correct response is:

x = 49.07 ft.