A 26 meter guy wire is attached to an upright pole 24 meters from the ground. How far from the pole must the wire be anchored in the ground?

a^2 + b^2 = c^2

24^2 + b^2 = 26^2

576 + b^2 = 676

b^2 = 100

b = 10 meters

x² = 26² - 24²

this is actually a Pythagorean triple...5-12-13
in this case...10-24-26

To find the distance from the pole where the wire must be anchored in the ground, we can apply the Pythagorean theorem. The Pythagorean theorem 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 acts as the hypotenuse, and the upright pole and the distance from the pole to the ground form the other two sides of the triangle.

Let's define the distance from the pole to the ground as x.

Using the Pythagorean theorem, we have:

x^2 + 24^2 = 26^2

Simplifying the equation:

x^2 + 576 = 676

Subtracting 576 from both sides:

x^2 = 100

Taking the square root of both sides:

x = 10

Therefore, the wire must be anchored in the ground 10 meters from the pole.

To find the distance from the pole where the guy wire must be anchored in the ground, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled 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 other two sides.

In this case, the guy wire represents the hypotenuse of the right-angled triangle, the upright pole represents one of the other sides, and the distance from the pole to the anchor point represents the other side. Let's call the distance from the pole to the anchor point "x."

So, using the Pythagorean theorem, we have:

x^2 + 24^2 = 26^2

Now, let's solve for x:

x^2 + 576 = 676 (by squaring 24 and 26)

x^2 = 676 - 576 (subtracting 576 from both sides)

x^2 = 100 (simplifying)

x = √100 (taking the square root of both sides)

x = 10 (evaluating the square root of 100)

Therefore, the guy wire must be anchored in the ground 10 meters away from the pole.