A zip line that is 170 ft long runs off the edge of a cliff and makes an angle of 29 degrees with the ground below. How far away from the wall of the cliff is the cable attached to the ground? Round to the nearest hundredths. (2 points)

Question

The cable is ___ feet away from the base of the cliff.

Answer 1

To find the distance from the wall of the cliff to the point where the cable touches the ground, we can use some basic trigonometry.

In this situation, we can use the cosine of the angle formed by the zip line and the ground.

The formula is:

\[ \text{adjacent} = \text{hypotenuse} \times \cos(\theta) \]

Where:

• The adjacent side is the distance from the base of the cliff to the point where the cable touches the ground.
• The hypotenuse is the length of the zip line (170 feet).
• \(\theta\) is the angle with the ground (29 degrees).

Plugging in the values:

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

Now we calculate \(\cos(29^\circ)\):

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

Now we can calculate the distance:

\[ \text{adjacent} \approx 170 \times 0.8746 \] \[ \text{adjacent} \approx 148.67 \]

Thus, rounding to the nearest hundredths, the cable is approximately 148.67 feet away from the base of the cliff.