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)
Responses
56 ft.
56 ft.
51 ft.
51 ft.
132 ft.
132 ft.
257 ft.
To find the horizontal distance from the base of the tower to where the zip line ends, we can use trigonometry.
Let x be the horizontal distance we are trying to find.
We are given that the angle of elevation when the zip line meets the ground is 65°. This means that the angle between the ground and the zip line is also 65°.
We can use the tangent function to find x:
tan(65°) = x/120
Cross multiplying, we get:
x = 120 * tan(65°)
Using a calculator, we find that tan(65°) is approximately 2.1445.
x ≈ 120 * 2.1445 = 257.34
Therefore, the horizontal distance from the base of the tower to where the zip line ends is approximately 257 feet.