Answer
The total length of cable required is \[30\text{ yd}\].
Work Step by Step
Let the height of flagpole till where the cable is attached be \[a\] and is calculated as:
\[\begin{align}
& a=\text{Height of flagpole}-\text{Distance between top of flagpole and cable point} \\
& =10\text{ yd}-4\text{ yd} \\
& =6\text{ yd}
\end{align}\]
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 one cable.
Hence, \[a=6\] and \[b=8\].
Compute the value of \[c\] by using Pythagorean Theorem and substitute the values of a and b into the equation as mentioned below:
\[\begin{align}
& {{c}^{2}}={{a}^{2}}+{{b}^{2}} \\
& ={{6}^{2}}+{{8}^{2}} \\
& =36+64 \\
& =100
\end{align}\]
Multiply both sides of the equation by \[\sqrt{{}}\]:
\[\begin{align}
& \sqrt{{{c}^{2}}}=\sqrt{100} \\
& c=10
\end{align}\]
Thus, the length of one cable is 10 yd.
The length of three cables can be computed as follows:
\[\begin{align}
& \text{Length of }3\text{ cables}=3\times \text{Length of }1\text{ cable} \\
& =3\times 10 \\
& =30\text{ yd}
\end{align}\]
Hence, the total length of cable required is \[30\text{ yd}\].
