A zip line that is 170 ft long runs off the edge of a cliff and makes an angle of 29 degrees with the gorund below. how far away from the wall of the cliff is the cable attached to the ground? Round to the nearest hundreths.

Answer 1

To find out how far away from the wall of the cliff the cable is attached to the ground, we can use some basic trigonometry. We know the length of the zip line (170 ft) and the angle it makes with the ground (29 degrees). We can determine the horizontal distance (adjacent side of the triangle) using the cosine function.

The formula we will use is:

\[ \text{horizontal distance} = \text{length of the zip line} \times \cos(\text{angle}) \]

Let's calculate the horizontal distance:

1. Convert the angle to radians if necessary, but since most calculators can work in degrees, we'll use degrees directly.
2. Plug in the values:

\[ \text{horizontal distance} = 170 \times \cos(29^\circ) \]

Using a calculator:

\[ \cos(29^\circ) \approx 0.8746 \]

Now substituting this value back into the equation:

\[ \text{horizontal distance} \approx 170 \times 0.8746 \approx 148.66 \text{ ft} \]

Rounding to the nearest hundredth, the horizontal distance from the wall of the cliff is approximately:

\[ \boxed{148.66} \text{ ft} \]

Answer 2

wrong whats the answer

Answer 3

Let's recalculate the horizontal distance correctly from the beginning.

Given:

• Length of the zip line (hypotenuse) = 170 ft
• Angle with the ground = 29 degrees

We want to find the horizontal distance (adjacent side) from the cliff using the cosine function:

\[ \text{horizontal distance} = \text{length of the zip line} \times \cos(\text{angle}) \]

So, we have:

\[ \text{horizontal distance} = 170 \times \cos(29^\circ) \]

Calculating the cosine of 29 degrees:

\[ \cos(29^\circ) \approx 0.8746 \]

Now calculate the horizontal distance:

\[ \text{horizontal distance} = 170 \times 0.8746 \approx 148.66 \text{ ft} \]

It appears the previous answer was indeed calculated correctly. The horizontal distance from the wall of the cliff is approximately:

\[ \boxed{148.66} \text{ ft} \]

If you believe there is a mistake, please clarify what part of the problem might be misunderstood, or if there are other parameters that may have changed!