A cable 22 feet long runs from the top of a utility pole to a point on the ground 15 feet from the base of the pole. How tall is the utility pole?

- thanks!

set up a right triangle

the base is 15, hypotenuse 22, and the height is x. solve for x.
use the pythagorean theorum.
a^2+b^2=c^2
15^2+x^2=22^2
225+x^2=484
x^2=259
x=16.09 feet

This looks like a problem for the Pythagorean Theorem.

a^2 + b^2 = c^2

15^2 + b^2 = 22^2
225 + b^2 = 484
b^2 = 484 - 225
b^2 = 259
b = 16.09 feet

To find the height of the utility pole, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the cable forms the hypotenuse of the right triangle, and the distance from the top of the pole to the ground forms one of the sides. Let's call the height of the pole "h."

Using the Pythagorean theorem, we have:

h^2 = 22^2 - 15^2

Simplifying, we get:

h^2 = 484 - 225

h^2 = 259

Taking the square root of both sides, we find:

h ≈ √259

h ≈ 16.09

Therefore, the height of the utility pole is approximately 16.09 feet.

To determine the height of the utility pole, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the cable forms the hypotenuse, and the distance from the base of the pole to the top of the pole forms one of the other two sides. The distance from the base of the pole to the point on the ground forms the remaining side.

Given that the cable is 22 feet long and the distance from the base of the pole to the point on the ground is 15 feet, you can set up the equation as follows:

height^2 + 15^2 = 22^2

Solving for height:
height^2 = 22^2 - 15^2
height^2 = 484 - 225
height^2 = 259
height ≈ √259
height ≈ 16.09 feet

Therefore, the utility pole is approximately 16.09 feet tall.