A guy wire is attached on the ground 100 feet from the base of the tower. The wire is also attached to the top of the 300 foot tower. How long is the guy wire?

Please learn the difference between geometry and geography!

Use the Pythagorean Theorem to find the hypotenuse.

To find the length of the guy wire, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the guy wire forms a right triangle with the ground and the tower. The distance from the base of the tower to the point where the guy wire touches the ground is the base of the triangle, which is given as 100 feet. The height of the triangle is the height of the tower, which is given as 300 feet. So, we need to find the length of the hypotenuse (the guy wire).

Using the Pythagorean theorem, we can write:

Hypotenuse^2 = Base^2 + Height^2

Let's substitute the given values:

Hypotenuse^2 = 100^2 + 300^2

Hypotenuse^2 = 10000 + 90000

Hypotenuse^2 = 100000

Taking the square root of both sides:

Hypotenuse = √100000

Hypotenuse ≈ 316.23 feet

Therefore, the length of the guy wire is approximately 316.23 feet.

To find the length of the guy wire, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the guy wire is the hypotenuse, and the two sides are the distance from the base of the tower to the point where the wire is attached on the ground (100 feet) and the height of the tower (300 feet).

The formula for the Pythagorean theorem is:

c^2 = a^2 + b^2

where c is the hypotenuse (length of the guy wire) and a and b are the other two sides.

Using this formula, we can substitute the given values:

c^2 = 100^2 + 300^2

c^2 = 10000 + 90000

c^2 = 100000

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

c = sqrt(100000)

c ≈ 316.227

Therefore, the length of the guy wire is approximately 316.227 feet.