Answer
Total length of cable required is\[45\text{ yards}\].
Work Step by Step
The height of flagpole is 16 yards which are supported by 3 cables attached to the flagpole and is 4 yards just below the flagpole. Also, the cable attached to the ground is at a distance of 9 yards from the base of the flagpole.
Let the height of flagpole till where the cable is attached be a and solve for the same using the equation as shown below.
\[\begin{align}
& a=\text{Height of flagpole}-\text{Distance between top of flagpole and cable point} \\
& a=16\text{ yards}-4\text{ yards} \\
& a=12\text{ yards}
\end{align}\]
Let b be the distance from the base of the flagpole to the point where the cable is attached to the ground and c be the length of 1 cable.
Hence, \[a=12\]and\[b=9\].
Compute the value of \[c\]by using Pythagorean Theorem and By using formula
\[\begin{align}
& {{c}^{2}}={{a}^{2}}+{{b}^{2}} \\
& {{c}^{2}}={{12}^{2}}+{{9}^{2}}
\end{align}\]
Now if\[{{12}^{2}}=12.12=144\], \[{{9}^{2}}=9.9=81\]then solve for c using the equation as shown below.
\[\begin{align}
& {{c}^{2}}=144+81 \\
& {{c}^{2}}=225 \\
& c=\sqrt{225} \\
& c=15 \\
\end{align}\]
Therefore, the length of 1 cable is 15 yards. Compute the length 3 cables as follows:
\[\begin{align}
& \text{Length of }3\text{ cables}=3\times \text{Length of }1\text{ cable} \\
& =3\times 15 \\
& =45\text{ yards}
\end{align}\]
Hence, the total length of cable required is\[45\text{ yards}\].
