Final answer:
Using trigonometry, the length of each cable is approximately 345.26 feet, and the distance from the base of the tower for the anchors is approximately 172.63 feet.
Step-by-step explanation:
To solve the problem of finding the length of the cables and the distance from the base of the tower, we can use trigonometry. We know the tower is 220 feet tall, and the angle the cables make with the ground is 52 degrees. We can model this situation using a right triangle where the tower is the opposite side, the distance from the base is the adjacent side, and the cable is the hypotenuse.
To find the length of the cable (hypotenuse), we use the cosine function:
cos(52°) = adjacent/hypotenuse
Rearrange the equation to solve for the cable length:
- cable length = (distance from base)/cos(52°)
Similarly, to find the distance from the base, we can use the tangent function:
- tan(52°) = opposite/adjacent
- tan(52°) = 220 feet/distance from base
So, the distance from the base is:
- distance from base = 220 feet/tan(52°)
Using a calculator, we can find that:
- cable length ≈ 220 feet/cos(52°) ≈ 345.26 feet
- distance from base ≈ 220 feet/tan(52°) ≈ 172.63 feet
Therefore, each cable must be approximately 345.26 feet long, and the anchors should be placed about 172.63 feet from the base of the tower.