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?
a. x = 29.38 ft.
b. x = 135.10 ft.
c. x = 12.74 ft.
d. x = 49.07 ft.

Answer 1

To find the horizontal distance \( x \) that the zipline will cover, we can use trigonometry. Specifically, we can use the tangent function, since we have the height of the zipline and the angle of elevation.

The relationship is given by:

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

In this case:
- \(\theta = 27^\circ\)
- The opposite side (the height of the zipline) = 25 feet
- The adjacent side (the horizontal distance \( x \)) is what we want to find.

Rearranging the formula gives us:

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

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

\[
\tan(27^\circ) \approx 0.5100
\]

Now, substituting this value into our equation:

\[
x \approx \frac{25}{0.5100} \approx 49.02 \text{ feet}
\]

Rounding it, we find:

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

So the answer is:

**d. \( x = 49.07 \text{ ft} \)**.