A guy wire stretches from a point on the ground 18 feet away from a vertical pole to the top of a 24 foot high pole. How many feet long is the guy wire?

This problem can be solved using 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.

Here, the pole is one side of the triangle, the distance from the pole to the point on the ground is the other side, and the guy wire is the hypotenuse.

Step 1: Identify the lengths of the two sides of the right triangle. The pole is 24 feet high (one side) and the distance from the pole to the point on the ground is 18 feet (the other side).

Step 2: Apply the Pythagorean theorem. The theorem is a^2 + b^2 = c^2, where c is the hypotenuse.

So, 24^2 + 18^2 = c^2 576 + 324 = c^2 900 = c^2

Step 3: Solve for c. Take the square root of both sides to solve for c.

c = sqrt(900) = 30 feet

So, the guy wire is 30 feet long.