Question

A cable is needed to support a vertical pole 24 feet high. The cable will be attached to the top of the pole and anchored to a stake 8 feet from the base of the pole. How much cable is needed? (Approximate to thenearest foot)

Answer 1

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

`c^2=a^2+b^2`

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

`\begin{gathered} c^2=a^2+b^2 \\ c^2=24^2+8^2 \\ c^2=576+64 \\ c^2=640 \\ √(c^2)=√(640) \\ c^{}=\sqrt[]{640} \\ c^{}=25.298 \\ c=25\; \; \text{feet} \end{gathered}`

Therefore, the required length of the cable is 25 feet. (to the nearest foot)