To find how far away from the wall of the cliff the cable is attached to the ground, we can use the relationship between the length of the zip line, the angle it makes with the ground, and the horizontal distance from the base of the cliff.
We use the cosine function in this case, as it relates the adjacent side (horizontal distance from the cliff) to the hypotenuse (length of the zip line):
\[ \text{horizontal distance} = \text{length} \times \cos(\theta) \]
Where:
- Length of the zip line = 170 ft
- Angle \(\theta = 29^\circ\)
Now we can plug in the values:
\[ \text{horizontal distance} = 170 \times \cos(29^\circ) \]
Calculating \(\cos(29^\circ)\):
\[ \cos(29^\circ) \approx 0.8746 \quad (\text{using a calculator}) \]
Now, substitute this value into the equation:
\[ \text{horizontal distance} = 170 \times 0.8746 \approx 148.66 \]
Rounding to the nearest hundredths, we get:
\[ \text{horizontal distance} \approx 148.66 \text{ feet} \]
Thus, the cable is approximately 148.66 feet away from the base of the cliff.
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