The length of the vertical pole is 24 feet.
The length between the pole and stake is 8 feet.
We are asked to find the length of the cable needed from the top of the pole and anchored to a stake.
Let us draw a sketch to better understand the problem.
Notice that it is a right-angled triangle, so we apply the Pythagorean theorem given by
[tex]c^2=a^2+b^2[/tex]Where c is the hypotenuse (length of the cable required)
a and b are the shorter legs (length of pole and the length between pole and stake)
a = 24 feet
b = 8 feet
Let us substitute these values into the above formula and solve for c
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=24^2+8^2 \\ c^2=576+64 \\ c^2=640 \\ \sqrt{c^2}=\sqrt{640} \\ c^{}=\sqrt[]{640} \\ c^{}=25.298 \\ c=25\; \; \text{feet} \end{gathered}[/tex]Therefore, the required length of the cable is 25 feet. (to the nearest foot)
