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?

x=49.07 ft
x=29.38 ft
x=12.74 ft
x=135.10 ft

Answer 1

To find the horizontal distance \( x \) that the zipline will cover, we can use the properties of right triangles. Given the height of the zipline (the vertical side) and the angle of elevation, we can use the tangent function.

1. **Identify the given values:**
- Height (opposite side) = 25 feet
- Angle of elevation (θ) = 27 degrees

2. **Using the tangent function:**
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where:
- Opposite = 25 feet (the height)
- Adjacent = \( x \) (the horizontal distance)

3. **Rearranging for \( x \):**
\[
x = \frac{\text{opposite}}{\tan(\theta)}
\]
\[
x = \frac{25}{\tan(27^\circ)}
\]

4. **Calculating \( \tan(27^\circ) \):**
The approximate value of \( \tan(27^\circ) \) is about 0.5095.

5. **Substituting the values:**
\[
x = \frac{25}{0.5095} \approx 49.07 \text{ feet}
\]

Thus, the horizontal distance the zipline will cover is approximately **49.07 feet**.

The correct answer is \( x = 49.07 \, \text{ft} \).