Substitute the known values in the given formula and simplify.
4108.6 feet
Practice makes perfect
We are given a formula which can be used to calculate the length for a wire attached to an antenna at a height h.
sqrt((h)^2 + (0.55h)^2)
We want to find the value of this expression for the three different heights given. We can substitute these values of h into the given expression and simplify following the order of operations. Let's start with h= 200.
Now, remember that the problem says that 3 wires are used at each height, so we need to multiply our result by 3.
(228.254244...) * 3 = 684.762732 ...
Let's round the result to the nearest tenth.
684. 7 62732≈ 684.8
We can follow the same process to find the total length of wire needed for the other heights.
h
sqrt((h)^2 + (0.55h)^2)
Simplified
* 3
Rounded to nearest tenth
200
sqrt(( 200)^2 + (0.55* 200)^2)
228.254244...
684.762732 ...
684.8
400
sqrt(( 400)^2 + (0.55* 400)^2)
456.508488...
1369.525465...
1369.5
600
sqrt(( 600)^2 + (0.55* 600)^2)
684.762732...
2054.288197...
2054.3
Finally, we need to add the lengths needed for each of the three heights to calculate the total amount of wire needed.
684.8 + 1369.5 + 2054.3 = 4108.6
Therefore, we need a minimum of 4108.6 feet of wire.
