Substitute x for the heights, and add the lengths of the wires.
A
a
About 306.27 feet
B
b
About 36.32^(∘)
C
c
sqrt(900+x^2)+sqrt(256+x^2)+sqrt(1156+x^2)
Practice makes perfect
a
Examining the diagram, we can identify three types of wires. Each type has the same length. We have highlighted each type of wire in the diagram below based on their length.
Let's isolate two of the wires that connect to the midpoint of the roof's sides. Since they cut the length of each side in half, we can create two right triangles where both legs are known.
When we know the length of the wires that connect to the midpoint, we can use either of them to calculate the length of the wires that connect to the roof's four corners.
Now we can calculate the total length of the wires by multiplying the length of each type of wire by how many there are in the picture and then adding the products.
If the antenna is x feet, we first have to redo all of the calculations from Part A that includes the height of the antenna.
30^2+x^2=( c_1)^2 ⇔ c_1=sqrt(900+x^2)
16^2+x^2=( c_2)^2 ⇔ c_2=sqrt(256+x^2)Next, we will calculate the length of the longest wire.
30^2+(sqrt(256+x^2))^2=( c_3)^2
⇕
c_3=sqrt(1156+x^2)
Now we can find the new length by adding c_1, c_2 and c_3.
c_1+ c_2+ c_3
⇕
sqrt(900+x^2)+ sqrt(256+x^2)+ sqrt(1156+x^2)
