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=12.74 ft.
x equals 12.74 ft.

x=135.10 ft.
x equals 135.10 ft.

x=29.38 ft.

Answer 1

To find the horizontal distance \( x \) that the zipline covers, we can use the given height and the angle of elevation.

We can visualize the situation as a right triangle where:

• the height (opposite side) is 25 feet,
• the angle of elevation is \( 27^\circ \),
• and the horizontal distance \( x \) is the adjacent side.

The tangent of the angle is given by the formula:

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

Plugging in the values we have:

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

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

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

Now, we need to calculate \( \tan(27^\circ) \). Using a calculator, we find:

\[ \tan(27^\circ) \approx 0.5108 \]

Substituting this back into our equation for \( x \):

\[ x \approx \frac{25}{0.5108} \approx 48.94 \text{ feet} \]

Rounding to two decimal places, we find:

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

Therefore, the correct response is:

x=49.07 ft.