In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance from the base of the antenna to the down point DOWN hill is 95 feet. Ignore the amount of cable needed to fasten the cable to the antenna or to the tie downs. How much cable is needed?
To find the amount of cable needed, we can use trigonometry. Since the antenna is anchored by two cables, we need to find the length of each cable.
First, let's visualize the problem. Imagine a right-angled triangle with the hill forming the inclined plane. The angle of 12 degrees is the angle between the hill and the horizontal ground. The distance from the base of the antenna to the down point down the hill is the hypotenuse of the triangle.
Using trigonometry, we can relate the angle, the hypotenuse, and the adjacent side of the triangle (which represents the length of each cable).
The formula we can use is:
cos(angle) = adjacent/hypotenuse
In this case, the angle is 12 degrees, and the hypotenuse (distance from the base to the down point down the hill) is 95 feet.
cos(12 degrees) = adjacent/95
Now, let's solve for the adjacent side (length of each cable):
adjacent = cos(12 degrees) * 95
Using a scientific calculator or trigonometric table, we can find the value of cos(12 degrees) as approximately 0.9781. Plugging this into the equation:
adjacent = 0.9781 * 95
Calculating this, we can find that each cable needs approximately 92.82 feet of length.
Therefore, the total amount of cable needed for both cables is 92.82 feet + 92.82 feet = 185.64 feet.
Approximately 185.64 feet of cable would be needed to anchor the antenna.