Question
The Tangent Ratio Quick Check 5 of 55 of 5 Items 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=135.10 ft. x equals 135.10 ft. x=49.07 ft. x equals 49.07 ft. x=29.38 ft. x equals 29.38 ft. Skip to navigation page 8 of 8
Answers
GPT-4o mini
To find the horizontal distance \( x \) the zipline covers, we can use the tangent ratio, which is defined as:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
In this case, the angle of elevation \( \theta \) is 27 degrees, the height (opposite side) is 25 feet, and we are trying to solve for the horizontal distance (adjacent side), which is \( x \).
Rearranging the tangent ratio gives us:
\[
\tan(27^\circ) = \frac{25}{x}
\]
Now, we can express \( x \) in terms of \( \tan(27^\circ) \):
\[
x = \frac{25}{\tan(27^\circ)}
\]
Next, we can calculate \( \tan(27^\circ) \):
\[
\tan(27^\circ) \approx 0.5108
\]
Now, substituting this value into the equation for \( x \):
\[
x = \frac{25}{0.5108} \approx 48.94 \text{ feet}
\]
Rounding this value gives us approximately \( 49.07 \) feet.
So, the correct response is:
**x = 49.07 ft.**
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
In this case, the angle of elevation \( \theta \) is 27 degrees, the height (opposite side) is 25 feet, and we are trying to solve for the horizontal distance (adjacent side), which is \( x \).
Rearranging the tangent ratio gives us:
\[
\tan(27^\circ) = \frac{25}{x}
\]
Now, we can express \( x \) in terms of \( \tan(27^\circ) \):
\[
x = \frac{25}{\tan(27^\circ)}
\]
Next, we can calculate \( \tan(27^\circ) \):
\[
\tan(27^\circ) \approx 0.5108
\]
Now, substituting this value into the equation for \( x \):
\[
x = \frac{25}{0.5108} \approx 48.94 \text{ feet}
\]
Rounding this value gives us approximately \( 49.07 \) feet.
So, the correct response is:
**x = 49.07 ft.**