A guy wire that is used to support a pole is attached at a height of 61 ft and at an angle of 68.1° above the ground. How far from the base of the pole is the guy wire attached to the ground?
a. 163.54 ft
c. 24.52 ft
b. 56.6 ft
d. 65.74 ft
To solve this problem, we can use trigonometry. Let's call the distance between the base of the pole and the point where the guy wire is attached to the ground "x."
Using trigonometry, we can determine that the height of the attachment point is given by the equation:
Height = x * tan(angle)
In this problem, the height is given as 61 ft, and the angle is given as 68.1°. Therefore, we can rewrite the equation as:
61 = x * tan(68.1°)
To find x, we can isolate it by dividing both sides of the equation by tan(68.1°):
x = 61 / tan(68.1°)
Using a calculator, we can determine that tan(68.1°) is approximately 2.511. Therefore:
x = 61 / 2.511
x ≈ 24.33 ft
Therefore, the guy wire is attached to the ground approximately 24.33 ft from the base of the pole.
The closest answer choice is option c. 24.52 ft.