A zipline starts 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°, what is the horizontal distance from the base of the tower to where the zip line ends?(1 point)

Question

Responses

56 ft.56 ft.

257 ft.257 ft.

51 ft.51 ft.

132 ft.

Answer 1

To find the horizontal distance from the base of the tower to where the zip line ends, we can use trigonometry. We know the vertical height (opposite side) and the angle of elevation.

Given:

• Height (opposite side) = 120 feet
• Angle of elevation (θ) = 65°

We can use the tangent function, which is defined as:

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Here, the opposite side is the height of the zipline (120 ft), and the adjacent side is the horizontal distance (d) that we are trying to find.

Rearranging the formula gives:

\[ \text{adjacent} = \frac{\text{opposite}}{\tan(\theta)} \]

Substituting the known values:

\[ d = \frac{120 \text{ ft}}{\tan(65^\circ)} \]

Now we calculate \(\tan(65^\circ)\):

\[ \tan(65^\circ) \approx 2.1445 \]

Now calculate the horizontal distance:

\[ d \approx \frac{120}{2.1445} \approx 55.8 \text{ ft} \]

Rounding gives us approximately 56 ft.

So, the horizontal distance from the base of the tower to where the zip line ends is 56 ft.