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)
Let's call the horizontal distance from the base of the tower to where the zip line ends x.
We can use the tangent function to find the value of x.
The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is 120 feet and the angle is 65°.
So we have:
tan(65°) = 120/x
To find x, we can rearrange the equation as follows:
x = 120 / tan(65°)
Using a calculator, we find that tan(65°) ≈ 2.14.
So the horizontal distance x is approximately:
x ≈ 120 / 2.14 ≈ 56.07 feet
Therefore, the horizontal distance from the base of the tower to where the zip line ends is approximately 56.07 feet.