Question
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
x=12.74 ft.
x equals 12.74 ft.
x=29.38 ft.
x equals 29.38 ft.
x=49.07 ft.
x equals 49.07 ft.
x=135.10 ft.
Answers
Answered by
GPT-4o mini
To find the horizontal distance \( x \) that the zipline will cover, we can use the properties of right triangles. We know:
- The height of the zipline (opposite side) is 25 feet.
- The angle of elevation is 27°.
We can use the tangent function, which relates the opposite side to the adjacent side:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{25}{x}
\]
Rearranging the formula to solve for \( x \):
\[
x = \frac{25}{\tan(27^\circ)}
\]
Now we calculate \( \tan(27^\circ) \):
\[
\tan(27^\circ) \approx 0.5095
\]
Now substituting this value into the equation for \( x \):
\[
x = \frac{25}{0.5095} \approx 49.07 \, \text{ft}
\]
Thus, the horizontal distance the zipline will cover is:
\[
\boxed{49.07 \, \text{ft.}}
\]
So the correct response is **x = 49.07 ft.**
- The height of the zipline (opposite side) is 25 feet.
- The angle of elevation is 27°.
We can use the tangent function, which relates the opposite side to the adjacent side:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{25}{x}
\]
Rearranging the formula to solve for \( x \):
\[
x = \frac{25}{\tan(27^\circ)}
\]
Now we calculate \( \tan(27^\circ) \):
\[
\tan(27^\circ) \approx 0.5095
\]
Now substituting this value into the equation for \( x \):
\[
x = \frac{25}{0.5095} \approx 49.07 \, \text{ft}
\]
Thus, the horizontal distance the zipline will cover is:
\[
\boxed{49.07 \, \text{ft.}}
\]
So the correct response is **x = 49.07 ft.**