how long is the cable that supports a 10m. high antenna if the cable is connected at the middle of the pole of the antenna and at the ground 6m. away from the base of the pole?
These are all just about the basic trig functions. Draw a diagram and just decide which function to use.
To determine the length of the cable supporting the antenna, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse (the cable) is equal to the sum of the squares of the other two sides (the height of the antenna and the distance from the base to the point where the cable is connected).
Let's break down the given information:
- The height of the antenna is 10m.
- The distance from the base of the pole to the ground point where the cable is connected is 6m.
Using the Pythagorean theorem, we can calculate the length of the cable:
Length of the cable squared = (Height of the antenna squared) + (Distance from the base to the point where the cable is connected squared)
Length of the cable squared = (10m^2) + (6m^2)
Length of the cable squared = 100m^2 + 36m^2
Length of the cable squared = 136m^2
To find the length of the cable, we take the square root of both sides:
Length of the cable = √136m^2
Length of the cable ≈ 11.66m
Therefore, the cable that supports a 10m high antenna, connected at the middle of the pole and 6m away from the base of the pole, is approximately 11.66 meters long.