To find the distance from the base of the tower to the point where the zip line meets the ground, we can use the concept of right triangles.
Given:
- Height of the zip line (the vertical side) = 120 feet
- We want to find the horizontal distance (the base) from the tower to where the zip line meets the ground.
Since we weren't provided with the angle of elevation at the zip line's end, let's denote it as \( \theta \). The relationship between the angle of elevation, the opposite side (height of 120 feet), and the adjacent side (distance along the ground) can be expressed using the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{120}{d} \]
Where \( d \) is the horizontal distance from the base of the tower to where the zip line meets the ground.
You would need the specific angle of elevation to calculate the exact distance. However, if we assume you have a specific angle \( \theta \), you could rearrange the equation as follows:
\[ d = \frac{120}{\tan(\theta)} \]
To provide a specific numerical example, if you were given that the angle of elevation \( \theta \) is \( 45^\circ \) (for example), then:
\[ \tan(45^\circ) = 1 \] \[ d = \frac{120}{1} = 120 \text{ feet} \]
Thus, the horizontal distance \( d \) would equal 120 feet in this case.
For any other angle, you would substitute the angle in the tangent function to calculate \( d \).
If you have a specific angle in mind, please share it for an exact calculation. Otherwise, you can use the equation provided to compute \( d \) for any given angle of elevation.
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