A wire to be attached to support a telephone pole. Because of surrounding buildings, sidewalks and roadways, the wire must be anchored exactly 21 feet from the base of the pole. Telephone company workers have only 28 feet of cable, and 2 feet of that must be attached to the cable to the pole and to the stake on the ground. How high from the base of the pole can the wire be attached.

The wire can be attached at the height of __ feet from the base of the poles.( simplify your answer)

The wire can be attached at the height of approximately ___ feet from the base of the pole. (Round to two decimal places as needed)

To find the height at which the wire can be attached, let's set up a right triangle with the pole as the base and the point where the wire is attached as the topmost point.

Let the distance from the base of the pole to the point where the wire is attached be h feet.

Given:
- The wire must be anchored exactly 21 feet from the base of the pole.
- Telephone company workers have only 28 feet of cable, and 2 feet of that must be attached to the cable to the pole and to the stake on the ground.

In the right triangle, the hypotenuse represents the total length of the wire available, which is 28 feet. The base is 21 feet, and the height is unknown (h).

Using the Pythagorean theorem:
(h)^2 + (21)^2 = (28)^2

Expanding and simplifying:
h^2 + 441 = 784

Subtracting 441 from both sides:
h^2 = 343

Taking the square root of both sides:
h = √343

Since √343 = 7√7, the height from the base of the pole at which the wire can be attached is 7√7 feet.

Approximating to two decimal places:
The wire can be attached at a height of approximately 16.55 feet from the base of the pole.

To solve this problem, we can use the Pythagorean Theorem. Let's call the height we are trying to find "h", the distance from the base of the pole to the attachment point on the wire "x", and the remaining length of the wire "y".

According to the problem, "x" is 21 feet and "y" is 28 - 2 = 26 feet (subtracting the 2 feet used to attach the cable to the pole and stake).

We can set up a right triangle with the pole as one side, the wire as the hypotenuse, and the distance from the base to the attachment point as the other side. Using the Pythagorean Theorem, we have:

x^2 + h^2 = y^2

Substituting the given values, we get:

21^2 + h^2 = 26^2
441 + h^2 = 676
h^2 = 676 - 441
h^2 = 235

To find "h", we take the square root of both sides:

h = √235

Therefore, the wire can be attached at a height of approximately √235 feet from the base of the pole.

To simplify further and find the approximate value, we can use a calculator:

h ≈ √235 ≈ 15.33

Therefore, the wire can be attached at the height of approximately 15.33 feet from the base of the pole.

So the support wire exposed can only be 26 ft

Clear case of Pythagoras
let the height be h, then
h^2 + 21^2 = 26^2
solve for h

Use Pythagoras's Theorem.

a^2 + b^2 = c^2

21^2 + b^2 = 26^2