Question

A wire is to be attached to support a telephone pole. Because of surrounding buildings sidewalks and roadways the wire must be anchored exactly 14 feet from the base of the pole. Telephone company workers have only 34 feet of cable and 5 feet of that must be used to attach the cable to the pile and to the stake on the ground. How high from the base of the pole can the wire be attachedThe wire can be attached at the weight of ? The weird can be attached at the height of approximately?

Answer 1

the wire can be attached at a height of √645 feet from the base of the pole.

the wire can be attached at a height of approximately 25.40 feet from the base of the pole.

Step-by-step explanation:

We know that the distance from the base of the pole is 14 feet. Additionally, the wire that they can use has a length of 29 feet because:

34 feet - 5 feet = 29 feet.

Now, we can represent the situation as follows:

So, we can see that there is a right triangle formed, where the heigh and the base are the legs and the wire is the hypotenuse.

Then, we can use the Pythagorean theorem to find the value of h, so:

`\begin{gathered} h=\sqrt[]{29^2-14^2} \\ h=\sqrt[]{841-196} \\ h=\sqrt[]{645} \\ h\approx25.40 \end{gathered}`

It means that the exact value for h is √645 and the approximation is 25.40

Therefore, the answers are:

the wire can be attached at a height of √645 feet from the base of the pole.

the wire can be attached at a height of approximately 25.40 feet from the base of the pole.