A zipline starts 120

120
feet above the ground and covers a diagonal distance, forming a triangle with the ground. If the angle of elevation where the zip line meets the ground is 65°
65
°
, what is the horizontal distance from the base of the tower to where the zip line ends?(1 point)
Responses

51 ft.
51

ft.
51 ft.
51

ft.

132 ft.
132

ft.
132 ft.
132

ft.

56 ft.
56

ft.
56 ft.
56

ft.

257 ft.

1 answer

To find the horizontal distance from the base of the tower to where the zip line ends, we can use the trigonometric relationship involving the angle of elevation, which is given by the tangent function:

\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]

where:

  • \(\theta\) is the angle of elevation (65°),
  • the opposite side is the height of the zip line above the ground (120 feet),
  • the adjacent side is the horizontal distance we want to find.

Rearranging the equation to solve for the horizontal distance (Adjacent):

\[ \text{Adjacent} = \frac{\text{Opposite}}{\tan(\theta)} \]

Substituting the values:

\[ \text{Adjacent} = \frac{120}{\tan(65°)} \]

Calculating the tangent of 65°:

\[ \tan(65°) \approx 2.1445 \]

Now substituting this value back into the equation:

\[ \text{Adjacent} = \frac{120}{2.1445} \approx 55.9 \text{ feet} \]

Rounding this result yields approximately 56 feet.

Therefore, the correct response is:

56 ft.