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)
O 51 ft.
© 257 ft.
O 56 ft.
O 132 ft.
We can use the trigonometric ratio tangent to solve this problem. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the tower (120 ft) and the angle of elevation (65°) is between the zip line and the ground. Therefore, the adjacent side is the horizontal distance from the base of the tower to where the zip line ends, which we need to find.
Using the tangent formula, we have:
tan(65°) = Opposite side / Adjacent side
tan(65°) = 120 ft / Adjacent side
To solve for the adjacent side, we can rearrange the equation:
Adjacent side = 120 ft / tan(65°)
Using a calculator, we can find the value of the tangent of 65°:
tan(65°) ≈ 2.14451
Now, we can substitute this value back into the equation:
Adjacent side ≈ 120 ft / 2.14451
Adjacent side ≈ 55.94 ft
Therefore, the horizontal distance from the base of the tower to where the zip line ends is approximately 56 ft.